axisymmetric solutions for the multi layered transversely isotropic piezoelectric medium by introducing the precise integration algorithm pia and the technique of the mixed variable formalism accounting for any number of layers variations of components of the axisymmetric piezoelectric field including elastic displacement vertical normal stress electric potential and electric displacement along the axis of symmetry in the cylindrical coordinate system are explored the piezoelectric field is induced by the vertical loadings of mechanical or electric types uniformly distributed over a circular region with the aid of the mixed variable formulations along with the hankel integral transform and the corresponding matrix algebraic operations the governing partial differential equations of equilibrium expressed in terms of displacements and electric potential are reduced to the first order ordinary differential matrix equations as a highly accurate algorithm the pia is provided to evaluate the obtained ordinary differential matrix equations in the transformed domain both mechanical and electrical quantities in the physical domain can be acquired by taking the inversion of the hankel integral transform an example as benchmark is illustrated to examine the applicability and performance of the proposed technique compared with results in the literature numerical examples are used to demonstrate the influence of the degree of the material anisotropy and stratified parameters

use of higher order shape functions in the scaled boundary finite element method the scaled boundary finite element method is a novel semi analytical technique whose versatility accuracy and efficiency are not only equal to but potentially better than the finite element method and the boundary element method for certain problems this paper investigates the possibility of using higher order polynomial functions for the shape functions two techniques for generating the higher order shape functions are investigated in the first the spectral element approach is used with lagrange interpolation functions in the second hierarchical polynomial shape functions are employed to add new degrees of freedom into the domain without changing the existing ones as in the p version of the finite element method to check the accuracy of the proposed procedures a plane strain problem for which an exact solution is available is employed a more complex example involving three scaled boundary subdomains is also addressed the rates of convergence of these examples under p refinement are compared with the corresponding rates of convergence achieved when uniform h refinement is used allowing direct comparison of the computational cost of the two approaches the results show that it is advantageous to use higher order elements and that higher rates of convergence can be obtained using p refinement instead of h refinement copyright 2005 john wiley sons ltd

unit impulse response matrix of unbounded medium by infinitesimal finite element cell method abstract to calculate the unit impulse response matrix of the unbounded medium the infinitesimal finite element cell method based solely on the finite element formulation and working exclusively in the time domain is developed a formulation can be derived for acceleration velocity and displacement unit impulse response matrices starting from the acceleration unit impulse impulse response matrix those of the velocity and displacement are constructed the algorithm to determine the acceleration unit impulse response matrix and its application are simpler than the other two alternatives as in the cloning algorithm the approach is based on similarity of the unbounded media corresponding to the interior and exterior boundaries of the infinitesimal finite element cell the derivation is performed exclusively in the time domain at each time station a linear system of equations is solved the consistent boundary method to analyse a layered medium in the frequency domain and the viscous dashpot boundary method are special cases of the infinitesimal finite element cell method the error is governed by the finite element discretization in the circumferential direction as the width of the finite element cell in the radial direction is infinitesimal the infinitesimal finite element cell method is thus exact in the finite element sense the method leads to highly accurate results for a vast class of problems ranging from a one dimensional spherical cavity to a rectangular foundation embedded in a half plane

consistent infinitesimal finite element cell method for diffusion equation in unbounded medium abstract to calculate the unit step response matrix of an unbounded medium for use in a time domain analysis of unbounded medium structure interaction for the diffusion equation the consistent infinitesimal finite element cell method is developed for the three dimensional case its derivation is based on the finite element formulation and on similarity the discretization is only performed on the structure medium interface yielding a reduction of the spatial dimension by 1 the procedure is rigorous in the radial direction and exact in the finite element sense in the circumferential directions in contrast to the boundary element procedure the consistent infinitesimal finite element cell method does not require a fundamental solution and incorporates interfaces extending from the structure medium interface to infinity compatible with similarity without any additional computational effort a general anisotropic material can be processed

wave propagation in anisotropic layered media the determination of the natural modes of wave propagation in an anisotropic layered medium requires the solution of a transcendental eigenvalue problem that is usually approached numerically with the aid of search techniques such computations require great effort the method presented in this paper provides an alternate solution to this problem in terms of a quadratic eigenvalue problem involving tridiagonal matrices for which the eigenvalues can be found with great speed and accuracy the technique is then illustrated by means of an example involving a cross anisotropic gibson solid

a finite element formulation in boundary representation for the analysis of nonlinear problems in solid mechanics abstract the contribution is concerned with a numerical element formulation in boundary representation it results in a polynomial element description with an arbitrary number of nodes on the boundary scaling the boundary description determines the interior domain the scaling approach is adopted from the so called scaled boundary finite element method sbfem which is a semi analytical formulation to analyze problems in linear elasticity within this method the basic idea is to scale the boundary with respect to a scaling center the boundary which is denoted as circumferential direction and the scaling direction span the parameter space in the present approach interpolations in scaling direction and circumferential direction are introduced the interpolation in circumferential direction is independent of the scaling direction the formulation is suitable to analyze problems in nonlinear solid mechanics the displacement degrees of freedom are located at the nodes on the boundary and in the interior element domain the degrees of freedom located at the interior domain are eliminated by static condensation which leads to a polygonal finite element formulation with an arbitrary number of nodes on the boundary the element formulation allows per definition for voronoi meshes and quadtree mesh generation numerical examples give rise to the performance of the present approach in comparison to other polygonal element formulations like the virtual element method vem some benchmark tests show the capability of the element formulation a comparison to standard and mixed element formulations is presented the present approach is perfectly suitable to model heterogeneous structures with inclusions and voids it avoids also staircase approximation of curved boundaries

a solvability theorem for a class of quasiconvex mappings with applications to optimization abstract in this paper a solvability theorem is proved for a class of quasiconvex mappings the solvability theorem is applied to characterize the local and global solutions of optimization problems where the mappings satisfy certain quasiconvexity conditions or their suitable approximations satisfy such conditions

a high order finite element technique with automatic treatment of stress singularities by semi analytical enrichment abstract this paper presents an approach to the automatic enrichment of finite elements in the vicinity of a stress singularity the enrichment consists of semi analytical singular modes constructed using the scaled boundary finite element method sbfem in contrast to analytical methods the sbfem provides modes for inhomogeneous and anisotropic materials without additional effort the finite element basis can be of arbitrary order and remains unaltered by the enrichment the approach requires enrichment in only one layer of elements around a node due to the compatibility of sbfem with fem there is no need for transitional elements and there are no parasitic terms the approach is tested for several benchmark problems the stress intensity factors are computed based on techniques inspired by the sbfem the proposed procedure is compared to a standard finite element implementation and shows a significant improvement in the error of the displacement field for problems involving singular stresses

on the stress wave imaging of cavities in a semi infinite solid the problem of mapping underground cavities from surface seismic measurements is investigated within the framework of a regularized boundary integral equation bie method with the ground modeled as a uniform elastic half space the inverse analysis of elastic waves scattered by a three dimensional void is formulated as a task of minimizing the misfit between experimental observations and theoretical predictions for an assumed void geometry for an accurate treatment of the gradient search technique employed to solve the inverse problem sensitivities of the predictive bie model with respect to cavity parameters are evaluated semi analytically using an adjoint problem approach and a continuum kinematics description several key features of the formulation including the rigorous treatment of the radiation condition for semi infinite solids modeling of an illuminating seismic wave field and treatment of the prior information are highlighted a set of numerical examples with spherical and ellipsoidal cavity geometries is included to illustrate the performance of the method it is shown that the featured adjoint problem approach reduces the computational requirements by an order of magnitude relative to conventional finite difference estimates thus rendering the three dimensional elastic wave imaging of solids tractable for engineering applications

scalar characterizations of weakly cone convex and weakly cone quasiconvex functions abstract the principal aim of this paper is to show that weakly cone convex vector valued functions as well as weakly cone quasiconvex vector valued functions can be characterized in terms of usual weakly convexity and weakly quasiconvexity of certain real valued functions defined by means of the extreme directions of the polar cone or by gerstewitz s scalarization functions

thin layer method formulation in the time domain the thin layer method is a semi discrete numerical technique that may be used for the dynamic analysis of laminated solids or fluids in its classical implementation the method is normally formulated in the frequency domain and requires the solution of a complex valued quadratic eigenvalue problem in this paper we present an alternative time domain formulation which can offer advantages in some cases such as avoiding the use of complex algebra the proposed method entails expressing the governing equations in the frequency wavenumber domain solving a linear real valued eigenvalue problem in the frequency variable carrying out an analytical integration over frequencies and performing a numerical transform over wavenumbers this strategy allows obtaining the green s functions for impulsive sources directly in the time domain even when the system has little or no damping we first develop the algorithm in its most general form allowing fully anisotropic materials and arbitrary expansion orders then we consider a restricted class of anisotropic materials for which the required linear eigenvalue problem involves only real narrowly banded symmetric matrices and finally we demonstrate the method by means of a simple problem involving a homogeneous stratum subjected to an antiplane impulsive source

the scaled boundary finite element method in structural dynamics the scaled boundary finite element method is extended to solve problems of structural dynamics the dynamic stiffness matrix of a bounded finite domain is obtained as a continued fraction solution for the scaled boundary finite element equation the inertial effect at high frequencies is modeled by high order terms of the continued fraction without introducing an internal mesh by using this solution and introducing auxiliary variables the equation of motion of the bounded domain is expressed in high order static stiffness and mass matrices standard procedures in structural dynamics can be applied to perform modal analyses and transient response analyses directly in the time domain numerical examples for modal and direct time domain analyses are presented rapid convergence is observed as the order of continued fraction increases a guideline for selecting the order of continued fraction is proposed and validated high computational efficiency is demonstrated for problems with stress singularity

scaled boundary polygons for linear elastodynamics abstract a polygonal scaled boundary finite element method sbfem is proposed for linear elastodynamics in two dimensions the domain is divided into non overlapping polygonal elements and the scaled boundary finite element approach is employed over each polygon the advantages are that an arbitrary interpolation order can be used on each polygon and we can choose the optimal element order on each edge individually moreover the sbfem simplifies the numerical integration over the polygons when compared to conventional approaches the dynamic stiffness matrix is computed by employing the continued fraction expansion the influence of the shape of the polygon and the element order on the boundary of each polygon are studied the robustness and the accuracy of the approach are demonstrated with numerical examples

on the general feasibility test of scheduling lot sizes for several products on one machine given n products and a set of basic data for each product e g production rate demand rate setup time setup cost and holding cost etc the economic lot scheduling problem is to find a feasible schedule that allows cyclic production pattern for each product and such that the sum of the setup and inventory carrying costs for all products per unit time is minimized the routine application of the economic lot size formula to each product separately often leads to the phenomenon of interference i e the machine will be required to produce two items at the same time which is impossible in this paper we show that even a very restricted version of the original problem becomes np hard we also give an implicit enumeration procedure for testing the feasibility of a schedule in which product i is set up i i integer times per year the main advantage of our procedure is that we can by pass the tedious study of the start times and concentrate on the combinatorial structure of the production runs which thus theoretically cuts down the number of possible branchings in the enumeration

a stochastic scaled boundary finite element method abstract by extending the existing scaled boundary finite element method sbfem into the random field problem a stochastic scaled boundary finite element method ssbfem is developed in this paper to predict the structural responses with randomly distributed material properties the analyzed domain is discretized into a number of polygons modeled as sub domains of the sbfem so that the non homogeneous material properties are possible to be considered in establishment of the constitutive equation the random field represented by the karhunen loeve kl expansion is then directly incorporated into both the equilibrium equation of the sbfem and its sensitivity analysis formulation the perturbation method is employed to calculate the statistical moments of the structural responses and a semi analytical sensitivity analysis method is used to efficiently calculate the gradients involved particularly the proposed method is successfully applied to the stochastic fracture analysis with spatially varying random material properties four numerical examples are investigated to demonstrate the validity of the proposed method

consistent infinitesimal finite element cell method three dimensional vector wave equation to calculate the unit impulse response matrix of an unbounded medium for use in a time domain analysis of unbounded medium structure interaction the consistent infinitesimal finite element cell method is developed for the three dimensional vector wave equation this is a boundary finite element procedure the discretization is only performed on the structure medium interface yielding a reduction of the spatial dimension by 1 the procedure is rigorous in the radial direction and exact in the finite element sense in the circumferential directions in contrast to the boundary element procedure the consistent infinitesimal finite element cell method does not require a fundamental solution and incorporates interfaces extending from the structure medium interface to infinity compatible with similarity without any additional computational effort a general anisotropic material can be processed the derivation is based on the finite element formulation and on similarity

explicit finite element perfectly matched layer for transient three dimensional elastic waves the use of a perfectly matched layer pml model is an efficient approach toward the bounded domain modelling of wave propagation on unbounded domains this paper formulates a three dimensional pml for elastic waves by building upon previous work by the author and implements it in a displacement based finite element setting the novel contribution of this paper over the previous work is in making this finite element implementation suitable for explicit time integration thus making it practicable for use in large scale three dimensional dynamic analyses an efficient method of calculating the strain terms in the pml is developed in order to take advantage of the lack of the overhead of solving equations at each time step the pml formulation is studied and validated first for a semi infinite bar and then for the classical soil structure interaction problems of a square flexible footing on a i half space ii layer on a half space and iii layer on a rigid base numerical results for these problems demonstrate that the pml models produce highly accurate results with small bounded domains and at low computational cost and that these models are long time stable with critical time step sizes similar to those of corresponding fully elastic models copyright 2008 john wiley sons ltd

efficient computation of order and mode of three dimensional stress singularities in linear elasticity by the boundary finite element method the boundary finite element method bfem a novel semi analytical boundary element procedure solely relying on standard finite element formulations is employed for the investigation of the orders and modes of three dimensional stress singularities which occur at notches and cracks in isotropic halfspaces as well as at free edges and free corners of layered plates after a comprehensive literature review and a concise introduction to the standard three dimensional bfem formulation for the static analysis of general unbounded structures we demonstrate the application of the bfem for the computation of the orders and modes of two dimensional and three dimensional stress singularities for several classes of problems within the framework of linear elasticity special emphasis is placed upon the investigation of stress concentration phenomena as they occur at straight free edges and at free corners of arbitrary opening angles in composite laminates in all cases the bfem computations agree excellently with available reference results the required computational effort is found to be considerably lower compared to e g standard finite element method fem computations in the case of free laminate corners numerous new results on the occurring stress singularities are presented it is found that free corner problems generally seem to involve a more pronounced criticality than the corresponding free edge situations

efficient wave propagation simulation on quadtree meshes using sbfem with reduced modal basis summary we apply a combination of the transient scaled boundary finite element method sbfem and quadtree based discretization to model dynamic problems at high frequencies we demonstrate that the current formulation of the sbfem for dynamics tends to require more degrees of freedom than a corresponding spectral element discretization when dealing with smooth problems on regular domains thus we improve the efficiency of the sbfem by proposing a novel approach to reduce the number of auxiliary variables for transient analyses based on this improved sbfem we present a modified meshing procedure which creates a quadtree mesh purely based on the geometry and allows arbitrary sizes and orders of elements as well as an arbitrary number of different materials the discretization of each subdomain is created automatically based on material parameters and the highest frequency of interest the transition between regions of different properties is straightforward when using the sbfem the proposed approach is applied to image based analysis with a particular focus on geological models this article is protected by copyright all rights reserved

a unified 3d based technique for plate bending analysis using scaled boundary finite element method summary this paper presents a unified technique for solving the plate bending problems by extending the scaled boundary finite element method the formulation is based on the three dimensional governing equation without enforcing the kinematics of plate theory only the in plane dimensions are discretised into finite elements any two dimensional displacement based elements can be employed the solution along the thickness is expressed analytically by using a matrix function the proposed technique is consistent with the three dimensional theory and applicable to both thick and thin plates without exhibiting the numerical locking phenomenon moreover the use of higher order spectral elements allows the proposed technique to better represent curved boundaries and to achieve high accuracy and fast convergence numerical examples of various plate structures with different thickness to length ratios demonstrate the applicability and accuracy of the proposed technique copyright 2012 john wiley sons ltd

unit impulse response of unbounded medium by scaled boundary finite element method to perform a dynamic analysis of a nonlinear structure interacting with an unbounded medium in the time domain it is desirable to formulate the interaction forces of the unbounded medium on the structure medium interface using displacements the corresponding response matrix to a unit impulse of displacements is calculated using the scaled boundary finite element method this method based solely on finite elements is very suitable to model an unbounded medium as the radiation condition at infinity is rigorously satisfied and the discretization is limited to the structure medium interface

diagonalization procedure for scaled boundary finite element method in modeling semi infinite reservoir with uniform cross section to improve the ability of the scaled boundary finite element method sbfem in the dynamic analysis of dam reservoir interaction problems in the time domain a diagonalization procedure was proposed in which the sbfem was used to model the reservoir with uniform cross section first sbfem formulations in the full matrix form in the frequency and time domains were outlined to describe the semi infinite reservoir no sediments and the reservoir bottom absorption were considered second a generalized eigenproblem consisting of coefficient matrices of the sbfem was constructed and analyzed to obtain corresponding eigenvalues and eigenvectors finally using these eigenvalues and eigenvectors to normalize the sbfem formulations yielded diagonal sbfem formulations a diagonal dynamic stiffness matrix and a diagonal dynamic mass matrix were derived an efficient method was presented to evaluate them in this method no riccati equation and lyapunov equations needed solving and no schur decomposition was required which resulted in great computational costs saving the correctness and efficiency of the diagonalization procedure were verified by numerical examples in the frequency and time domains but the diagonalization procedure is only applicable for the sbfem formulation whose scaling center is located at infinity copyright 2009 john wiley sons ltd

sensitivity analysis of the scaled boundary finite element method for elastostatics abstract as a semi analytical structural analysis algorithm the scaled boundary finite element method sbfem only discretizes the boundary of the analyzed domain without the need of fundamental solutions which makes it powerful for problems with stress singularity or unbounded foundation media in this paper a sensitivity analysis method of sbfem is proposed for elastostatics through which the first order derivatives of the structural responses with respect to the design parameters can be obtained efficiently and accurately an approach is suggested to compute the eigenvalue and eigenvector sensitivities of the hamilton matrix which are then used to calculate the analytical derivative of the stiffness matrix based on these calculations the sensitivities of displacements and stresses are further obtained by a series of differential equations the proposed sensitivity analysis method is also applied to the fracture mechanics problems three numerical examples are investigated to demonstrate the validity of the proposed method

consistent infinitesimal finite element cell method in plane motion note 189 reference lch article 1995 005 record created on 2007 04 24 modified on 2016 08 08

the stochastic galerkin scaled boundary finite element method on random domain summary the research work extends the scaled boundary finite element method sbfem to non deterministic framework defined on random domain wherein random behaviour is exhibited in the presence of the random field uncertainties the aim is to blend the sbfem into the galerkin spectral stochastic methods which leads to a proficient procedure for handling the stress singularity problems and crack analysis the young s modulus of structures is considered to have random field uncertainty resulting in the stochastic behaviour of responses mathematical expressions and the solution procedure are derived to evaluate the statistical characteristics of responses displacement strain and stress and stress intensity factors of cracked structures the feasibility and effectiveness of the presented method are demonstrated by particularly chosen numerical examples this article is protected by copyright all rights reserved

generalized convex set valued maps abstract the aim of this paper is to show that under a mild semicontinuity assumption the so called segmentary epi closedness the cone convex respectively cone quasiconvex set valued maps can be characterized in terms of weak cone convexity respectively weak cone quasiconvexity i e the notions obtained by replacing in the classical definitions the conditions of type for all x y in the domain and for all t in 0 1 by the corresponding conditions of type for all x y in the domain there exists t in 0 1

the scaled boundary finite element method analytical solution in frequency domain the scaled boundary finite element equation a system of ordinary differential equations in the radial coordinate is solved analytically applying a series expansion an eigenvalue problem of a hamiltonian matrix is solved when the difference of two eigenvalues is an even number besides the power series logarithmic functions occur two sets of independent solutions are obtained the scaled boundary finite element method is thus a semi analytical procedure to solve partial differential equations with the polynomial approximation of finite elements in the two circumferential directions and a closed form solution in the radial direction applications to bounded and unbounded domains demonstrate excellent accuracy

hybrid collocation galerkin approach for the analysis of surface represented 3d solids employing sb fem abstract this paper presents a numerical method to solve the three dimensional elasticity problem of surface represented solids a surface oriented formulation is derived in which the three dimensional solid is described by its boundary surfaces and a radial scaling center scaling the boundary surfaces with respect to the scaling center yields a parameterization of the complete solid the definition of the boundary surfaces is sufficient for the description of the solid thus the formulation conforms ideally to the boundary representation modeling technique used in cad in the present approach no tensor product structure of three dimensional objects is exploited to parameterize the physical domain the weak form of the equation of motion and the weak form of the neumann boundary conditions are enforced only at the boundary surfaces it leads to a transformation of the governing partial differential equations of elasticity to an ordinary differential equation ode of euler type solving the ode leads to the displacement in the radial scaling direction in the present approach the isogeometric galerkin finite element method is employed to describe the geometry of the boundary surfaces and also to approximate the displacement response of the boundary surfaces it exploits two dimensional nurbs objects to parameterize the boundary surfaces the final euler type ode is solved by the nurbs based collocation method the displacement response in the radial scaling direction is approximated by the nurbs basis functions hence the method can be extended to nonlinear problems the accuracy of the method is validated against analytical solutions in general the proposed formulation is able to model solids bounded by an arbitrary number of surfaces

a semi analytical curved element for linear elasticity based on the scaled boundary finite element method summary this work introduces a semi analytical formulation for the simulation and modeling of curved structures based on the scaled boundary finite element method sbfem this approach adapts the fundamental idea of the sbfem concept to scale a boundary to describe a geometry until now scaling in sbfem has exclusively been performed along a straight coordinate that enlarges shrinks or shifts a given boundary in this novel approach scaling is based on a polar or cylindrical coordinate system such that a boundary is shifted along a curved scaling direction the derived formulations are used to compute the static and dynamic stiffness matrices of homogeneous curved structures the resulting elements can be coupled to general sbfem or fem domains for elastodynamic problems computations are performed in the frequency domain results of this work are validated using the global matrix method and standard finite element analysis copyright 2016 john wiley sons ltd

isogeometric analysis enhanced by the scaled boundary finite element method abstract by leveraging the information of a typical cad model in the analysis the intensive process of discretization can be circumvented this unification has led to the isogeometric analysis iga hughes et al 2005 however as the cad model provides information only of the boundary a 2d 3d stress analysis is still one major step away in this work the concepts of isogeometric analysis and the scaled boundary finite element method sbfem are combined the sbfem requires only the boundary information and hence provides a seamless integration with the cad modeling within the proposed framework the nurbs basis functions are used to discretize the unknown fields in the circumferential direction whilst analytical solution is sought in the radial direction we further extend the framework to problems with singularities and to dynamic analysis the accuracy and the convergence properties of the proposed method are demonstrated with benchmark problems in the context of linear elasticity and linear elastic fracture mechanics

scaled boundary polygons with application to fracture analysis of functionally graded materials summary this study presents a framework for the development of polygon elements based on the scaled boundary fem underpinning this study is the development of generalized scaled boundary shape functions valid for any n sided polygon these shape functions are continuous inside each polygon and across adjacent polygons for uncracked polygons the shape functions are linearly complete for cracked polygons the shape functions reproduce the square root singularity and the higher order terms in the williams eigenfunction expansion this allows the singular stress field in the vicinity of the crack tip to be represented accurately using these shape functions a novel scaled boundary polygon formulation that captures the heterogeneous material response observed in functionally graded materials is developed the stiffness matrix in each polygon is derived from the principle of virtual work using the scaled boundary shape functions the material heterogeneity is approximated in each polygon by a polynomial surface in scaled boundary coordinates the intrinsic properties of the scaled boundary shape functions enable accurate computation of stress intensity factors in cracked functionally graded materials directly from their definitions the new formulation is validated and its salient features are demonstrated using five numerical benchmarks copyright 2014 john wiley sons ltd

a time domain solution for complex multilayered soil model with circular inhomogeneity by the sbfem the scaled boundary finite method sbfem is developed for analyzing wave propagation problem in the two dimensional unbounded domain with rigid bedrock it combines the advantages of the finite element method and boundary element boundary method moreover the original scaling center is replaced by a scaling line which is more suitable for analyzing the multilayered soil model therefore the modified sbfem develops the original sbfem a new derivation of the modified sbfem equation is built in the frame of hamilton system a continued fraction solution of the dynamic stiffness of the soil model with bedrock is obtained for the first time then by introducing the continued fraction solution and auxiliary variables it leads to the model resting on bedrock can be solved in time domain the global equation of motion is solved by the efficient precise time integration method this integral method is firstly employed in the modified sbfem the precision of the proposed method can achieve computer precision therefore an extremely efficient and accurate solution of the modified sbfem in time domain is obtained the results of the complex soil model with circular inhomogeneity show that the proposed method yields excellent results and high accuracy is observed

the scaled boundary finite element method a fundamental solution less boundary element method in this boundary element method based on finite elements only the boundary is discretized with surface finite elements yielding a reduction of the spatial dimension by one no fundamental solution is necessary and thus no singular integrals must be evaluated and general anisotropic material can be analysed for an unbounded semi infinite or infinite medium the radiation condition at infinity is satisfied exactly no discretization of free and fixed boundaries and interfaces between different materials is required the semi analytical solution inside the domain leads to an efficient procedure to calculate the stress intensity factors accurately without any discretization in the vicinity of the crack tip body loads are included without discretization of the domain thus the scaled boundary finite element method not only combines the advantages of the finite element and boundary element methods but also presents appealing features of its own after discretizing the boundary with finite elements the governing partial differential equations of linear elastodynamics are transformed to the scaled boundary finite element equation in displacement a system of linear second order ordinary differential equations with the radial coordinate as independent variable which can be solved analytically introducing the definition of the dynamic stiffness a system of nonlinear first order ordinary differential equations in dynamic stiffness with the frequency as independent variable is obtained besides the displacements in the interior the static stiffness and mass matrices of a bounded medium and the dynamic stiffness and unit impulse response matrices of an unbounded medium are calculated

numerical solutions for magneto electro elastic laminated plates resting on winkler foundation or elastic half space abstract this article investigates the bending response performances of the magneto electro elastic mee laminated plates resting on the winkler foundation or the elastic half space subjected to a transverse mechanical loading by assuming that the foundation is not electrically and magnetically conductive the scaled boundary finite element method sbfem based on the three dimensional 3d theory of elasticity is applied for both the simulation of the mee laminated plate and the elastic half space the sbfem model considers the generalized displacement involving the elastic displacement electric potential and magnetic potential as the nodal degree of freedom for the mee laminated plates and only the in plane of the mee laminated plate or the boundary of the elastic half space needs to be discretized leading to reduce the spatial dimension by one furthermore in the sbfem the governing equations can be solved by using an analytical approach in the radial direction of the scaled coordinate system so that it is particularly suitable for the simulation of the elastic half space for the winkler foundation plate system the global stiffness coupling governing equation that includes the interaction between the mee laminated plate and the winkler foundation is derived directly from the 3d elasticity equations of the mee laminated plate by assuming that the foundation reactions are proportional to the transverse displacements of the plate structure while for the mee laminated plate half space system the whole domain is divided into three sub domains including the mee laminated plate structure the near and semi infinite far foundation systems based on the sub structure method and then the stiffness matrix of each sub domain can be determined by means of the sbfem as a result the global stiffness equation of the plate half space system can be assembled according to the principle of the degree of freedom matching at the same nodes the numerical results obtained for limiting cases by using the proposed method were compared with the published works and showed excellent agreements with the solutions based on the analytical and numerical approaches so that the accuracy and applicability of the proposed formulations for the analysis of the interaction problems between the mee laminated plate and the winkler foundation or elastic half space can be verified moreover several numerical examples with various material properties geometries stacking sequences aspect ratios and supported boundary conditions were presented to show the effects of which on the responses of the plate foundation system

a numerical approach for the computation of dispersion relations for plate structures using the scaled boundary finite element method abstract in this paper a method is presented for the numerical computation of dispersion properties and mode shapes of guided waves in plate structures the formulation is based on the scaled boundary finite element method the through thickness direction of the plate is discretized in the finite element sense while the direction of propagation is described analytically this leads to a standard eigenvalue problem for the calculation of wave numbers the proposed method is not limited to homogeneous plates multi layered composites as well as structures with continuously varying material parameters in the direction of thickness can be modeled without essential changes in the formulation higher order elements have been employed for the finite element discretization leading to excellent convergence for complex structures it is shown by numerical examples that this method provides highly accurate results with a small number of nodes while avoiding numerical problems and instabilities

the scaled boundary finite element method alias consistent infinitesimal finite element cell method for diffusion note 264 reference lch article 1999 008doi 10 1002 sici 1097 0207 19990810 45 10 3 0 co 2 eview record in web of science record created on 2007 04 24 modified on 2016 08 08

a matrix function solution for the scaled boundary finite element equation in statics the scaled boundary finite element method is a fundamental solution less boundary element method based on finite elements it leads to semi analytical solutions for displacement and stress fields which permits problems with singularities or in infinite domains to be handled conveniently and accurately however the present eigenvalue method for solving the scaled boundary finite element equation requires additional treatments for multiple eigenvalues with parallel eigenvectors which results from logarithmic terms in the solutions a matrix function solution for the scaled boundary finite element equation in statics is presented in this paper it is numerically stable for multiple or near multiple eigenvalues as it is based on real schur decomposition power functions logarithmic functions and their transitions as occurring in fracture mechanics composites and two dimensional unbounded domains are represented semi analytically no a priori knowledge on the types and orders of singularity are required when simulating stress singularities

scaled boundary parametrizations in isogeometric analysis abstract this paper deals with a special class of parametrizations for isogeometric analysis iga the so called scaled boundary parametrizations are easy to construct and particularly attractive if only a boundary description of the computational domain is available the idea goes back to the scaled boundary finite element method sb fem which has recently been extended to iga we take here a different viewpoint and study these parametrizations as bivariate or trivariate b spline functions that are directly suitable for standard galerkin based iga our main results are first a general framework for this class of parametrizations including aspects such as smoothness and regularity as well as a generalization to domains that are not star shaped second using the poisson equation as an example we explain the relation between standard galerkin based iga and the scaled boundary iga by means of the laplace beltrami operator and derive an equivalence theorem further results concern the separation of integrals in both approaches and an analysis of the singularity in the scaling center among the computational examples we present a rotor geometry that stems from a screw compressor machine and compare different parametrization strategies

the computation of dispersion relations for three dimensional elastic waveguides using the scaled boundary finite element method abstract in this paper a numerical approach for the computation of dispersion relations for three dimensional waveguides with arbitrary cross section is proposed the formulation is based on the scaled boundary finite element method sbfem it is an extension of the approach previously derived for plate structures it is shown that the wavenumbers of guided waves in a waveguide can be obtained as the eigenvalues of the z matrix which is well known in the sbfem the hamiltonian properties of this matrix are utilized to derive an efficient way to compute the group velocities of propagating waves as eigenvalue derivatives the cross section of the waveguide is discretized using higher order spectral elements it is discussed in detail how symmetry axes can be utilized to reduce computational costs in order to sort the solutions at different frequencies a mode tracking algorithm is proposed based on the pade expansion

unit impulse response matrix of unbounded medium by finite element based forecasting note 172 reference lch article 1995 003doi 10 1002 nme 1620380702 record created on 2007 04 24 modified on 2016 08 08

a modified scaled boundary finite element method for three dimensional dynamic soil structure interaction in layered soil summary this paper is devoted to the analysis of elastodynamic problems in 3d layered systems which are unbounded in the horizontal direction for this purpose a finite element model of the near field is coupled to a scaled boundary finite element model sbfem of the far field the sbfem is originally based on describing the geometry of a half space or full space domain by scaling the geometry of the near field far field interface using a radial coordinate a modified form of the sbfem for waves in a 2d layer is also available none of these existing formulations can be used to describe a 3d layered medium in this paper a modified sbfem for the analysis of 3d layered continua is derived based on the use of a scaling line instead of a scaling centre a suitable scaled boundary transformation is proposed the derivation of the corresponding scaled boundary finite element sbfe equations in displacement and stiffness is presented in detail the latter is a nonlinear differential equation with respect to the radial coordinate which has to be solved numerically for each excitation frequency considered in the analysis various numerical examples demonstrate the accuracy of the new method and its correct implementation these include rigid circular and square foundations embedded in or resting on the surface of layered homogeneous or inhomogeneous 3d soil deposits over rigid bedrock hysteretic damping is assumed in some cases the dynamic stiffness coefficients calculated using the proposed method are compared with analytical solutions or existing highly accurate numerical results copyright 2011 john wiley sons ltd

mass lumping techniques in the spectral element method on the equivalence of the row sum nodal quadrature and diagonal scaling methods abstract in the context of wave propagation analysis the spectral element method sem in conjunction with a diagonal mass matrix is often the method of choice therefore it is of high importance to investigate the influence of different mass lumping schemes on the accuracy of the numerical results to this end we compare the performance of three established methods including the row sum method the nodal quadrature method and the diagonal scaling method the theoretical analysis of these methods reveals a close connection between them under certain conditions that are discussed in detail in this article we are able to show a direct equivalence between these three approaches in this regard the attainable accuracy of the numerical integration of the mass matrix plays an important role by means of several dynamic benchmark problems we verify the theoretical results and illustrate the convergence properties of the lumped mass matrix sem in comparison to a formulation based on the consistent mass matrix

a scaled boundary finite element method for modelling crack face contact problems abstract in the case of arbitrary traction on the side faces of an object a polynomial function of the radial coordinate can be employed to describe the side face loads using the scaled boundary finite element method sbfem a sbfem shape function considering the side face loads is presented together with the corresponding stiffness matrix and equivalent node load the lagrange multiplier method is used to establish the contact model between the crack faces the elements corresponding to the crack faces are divided into non crack tip elements and crack tip elements for the former the crack is designated the boundary of the polygonal sbfem element the contact tractions on the boundary are assigned to the nodes where the lagrange multiplier is applied for the point constraints for the latter the lagrange multiplier is assumed to be linear on the side faces for the segment constraints numerical examples demonstrate the validity of the proposed sbfem in addressing the crack face contact problem

the scaled boundary finite element method alias consistent infinitesimal finite element cell method for elastodynamics the scaled boundary finite element method alias the consistent infinitesimal finite element cell method is developed starting from the governing equations of linear elastodynamics only the boundary of the medium is discretized with surface finite elements yielding a reduction of the spatial dimension by one no fundamental solution is necessary and thus no singular integrals must be evaluated general anisotropic material is analysed without any increase in computational effort boundary conditions on free and fixed surfaces and on interfaces between different materials are enforced exactly without any discretization this method is exact in the radial direction and converges to the exact solution in the finite element sense in the circumferential directions for a bounded medium symmetric static stiffness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption a stress singularity is represented very accurately as the condition on the boundary in the vicinity of the point of singularity is satisfied without spatial discretization

a hybrid meshless local petrov galerkin method for unbounded domains abstract meshless methods have gained popularity in recent years however like the finite element method they do not handle unbounded domains well coupling with other techniques more suited to performing this task is problematic since nodal values on the boundary are fictitious rather than actual the scaled boundary finite element method is a semi analytical approach to computational mechanics ideally suited to modelling unbounded domains recently a meshless version of the scaled boundary method based on the local petrov galerkin approach has been developed this paper couples the meshless scaled boundary method used to model the far field with conventional meshless local petrov galerkin modelling of the near field the coupling method is general and could be applied to other techniques of modelling the far field such as the infinite element method

feasibility of scheduling lot sizes of three products on one machine this paper considers the economic lot scheduling problem that is the problem of finding a feasible schedule that allows cyclic production of several products on a single facility so as to minimize holding and set up costs we consider the case when three products are required to be produced in a given fixed lot size and at regular intervals we derive a very simple test for existence of a feasible schedule and a method of constructing feasible schedules if one exists the approach is simpler than the mixed integer programming approach and enumeration schemes currently proposed in the literature and is constructive

the use of genetic algorithms to solve the economic lot size scheduling problem the purpose of this paper is to investigate the use genetic algorithms gas for solving the economic lot size scheduling problem elsp the elsp is formulated using the basic period bp approach which results in a problem having one continuous decision variable and a number of integer decision variables equal to the number of products being produced this formulation is ideally suited for using gas the ga is tested on bomberger s classical problem the resulting solutions were better than those obtained using an iterative dynamic programming dp approach the total cost of ga solutions to the problem with utilization up to 65 were within 3 4 of the lower bound the ga also performed well for higher utilization yielding solutions within 13 87 of the lower bound for utilization up to 86 the ga was tested on a 30 item problem and good solutions were obtained the results of the ga under different binary representations crossover methods and initialization methods are compared to identify the best settings the results indicate that for this particular problem binary representation works better than gray coding 2 point crossover is best and an infeasible starting population is better than feasible