shape design sensitivity analysis for geometrically and materially nonlinear problems by the boundary element method abstract this paper is concerned with the determination of design sensitivity coefficients dscs for fully nonlinear problems i e problems with both material and geometric nonlincarities in solid mechanics the clastic strains arc assumed to be small but the nonclastic plastic or viscoplustic strains as well as rotations can be arbitrarily large dscs here refer to rates of change of response variables such as displacements or stresses in a deforming solid body with respect to parameters called design variables that define the initial undeformed shape of the body these dscs are history dependent the direct differentiation approach dda of the relevant derivative boundary element method dbem formulation is employed to obtain the dscs a general computer program is developed for the analysis of two dimensional plane strain and plane stress problems numerical results are obtained for illustrative problems and arc compared against direct solutions the results from the two methods agree almost perfectly for these problems this research has potential applications in the optimization of manufacturing processes such as extrusion rolling or forging

design sensitivities in problems involving material and geometric nonlinearities abstract the subject of this paper is the determination of design sensitivity coefficients dscs for linear elasticity and nonlinear both material and geometric problems in solid mechanics dscs here refer to rates of change of response variables such as displacements or stresses in a deforming solid body with respect to parameters called design variables that control the initial undeformed shape of the body in nonlinear problems these dscs are history dependent the direct differentiation approach dda of the relevant derivative boundary element method dbem formulation is employed here to obtain the dscs modelling of sharp corners on the boundary of a body is given special attention here numerical results are presented for illustrative examples the numerically obtained sensitivities even for stresses on the boundary of a body are shown in general to be very accurate typically it is difficult to obtain dscs for boundary stresses accurately by other methods yet they are very useful for optimal shape design of bodies ongoing research is currently focused on numerical calculation of dscs for large deformation problems and use of these dscs in process optimization an important future application area of this work is optimal design of manufacturing processes such as extrusion or forging

boundary integral equations for recovery of design sensitivities in shape optimization a new formulation for obtaining design sensitivities in shape optimization has been developed the formulation is based on a direct application of the material derivative concept to the appropriate boundary integral equations for displacements and stresses in an elastic solid as a check on accuracy the approach was applied to a uniformly loaded infinite plate containing an elliptical hole in this case the availability of an analytical solution made it possible to calculate errors exactly furthermore a wide range of stress states could be considered simply by varying the aspect ratio of the elliptical hole for convenience the design sensitivities were calculated with respect to changes in the major axis numerical convergence was established by comparing results based on four successive boundary meshes in general the predictions for both displacement and stress sensitivities were remarkably accurate

application of he s homotopy perturbation method for solving the cauchy reaction diffusion problem in this paper the solution of cauchy reaction diffusion problem is presented by means of the homotopy perturbation method reaction diffusion equations have special importance in engineering and sciences and constitute a good model for many systems in various fields application of homotopy perturbation method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution

iterative solution techniques in boundary element analysis iterative techniques for the solution of the algebraic equations associated with the direct boundary element analysis bea method are discussed continuum structural response analysis problems are considered employing single and multi zone boundary element models with and without zone condensation the impact on convergence rate and computer resource requirements associated with the sparse and blocked matrices resulting in multi zone bea is studied both conjugate gradient and generalized minimum residual preconditioned iterative solvers are applied for these problems and the performance of these algorithms is reported included is a quantification of the impact of the preconditioning utilized to render the boundary element matrices solvable by the respective iterative methods in a time competitive with direct methods to characterize the potential of these iterative techniques we discuss accuracy storage and timing statistics in comparison with analogous information from direct sparse blocked matrix factorization procedures matrix populations that experience block fill in during the direct decomposition process are included with different degrees of preconditioning iterative equation solving is shown to be competitive with direct methods for the problems considered

sensitivity analysis formulation for three dimensional conduction heat transfer with complex geometries using a boundary element method a special boundary integral formulation had been proposed to analyse many engineering problems of conduction heat transfer in complex three dimensional geometries closely spaced surface and circular hole in infinite domain or simple modification of it by rezayat and burton one example of such geometries is the mold sets in the injection molding process in this paper an efficient and accurate approach for the design sensitivity analysis dsa is presented for these kinds of problems in the similar complex geometries using the direct differentiation approach dda based on the above special boundary integral formulation the present approach utilizes the implicit differentiation of the boundary integral equations with respect to the design variables radii and locations of circular holes to yield the sensitivity equations a sample problem heat transfer of injection molding cooling system is solved to demonstrate the accuracy of the present sensitivity analysis formulation although the techniques introduced here are applied to a particular problem in heat transfer of injection molding cooling system their potential application is quite broad

isogeometric boundary element method for calculating effective property of steady state thermal conduction in 2d heterogeneities with a homogeneous interphase abstract based on the generalized self consistent scheme gscs the isogeometric boundary element method igabem is used to calculate the effective thermal conductivity of two dimensional 2d steady state heat conduction heterogeneities with a homogeneous interphase the heat energy formulation and the boundary integral equations adopted in this paper only contain the temperatures from the inclusion interphase and interphase matrix interfaces respectively so that the effective thermal conductivity from the generalized self consistent model with a homogeneous interphase can be conveniently calculated in numerical implementation the non uniform rational b splines nurbs are employed not only to construct the exact interface shapes but also to approximate the interface temperatures the results show that the conductivity and the thickness of the homogeneous interphase have great influence on the effective thermal conductivity higher interphase thermal conductivity enhances the effective thermal conductivity whereas thinner thickness of the interphase results in the reduction of the effective thermal conductivity numerical examples show that the proposed method works well compared with the conventional quadratic isoparametric boundary element method

a bem sensitivity and shape identification analysis for acoustic scattering in fluid solid problems in this paper a boundary element formulation for the sensitivity analysis of structures immersed in an inviscide fluid and illuminated by harmonic incident plane waves is presented also presented is the sensitivity analysis coupled with an optimization procedure for analyses of flaw identification problems the formulation developed utilizes the boundary integral equation of the helmholtz equation for the external problem and the cauchy navier equation for the internal elastic problem the sensitivities are obtained by the implicit differentiation technique examples are presented to demonstrate the accuracy of the proposed formulations 1998 john wiley sons ltd

sensitivity analysis and optimal design in charge transport problems the focus of this paper is the accurate and efficient determination of sensitivities of electrostatic potential and charge density in charge transport problems and the use of these sensitivities to carry out optimal design direct differentiations of the boundary integral formulation of poisson s equation for charge conservation and of the non linear partial differential equation for current continuity are carried out to obtain equations satisfied by the sensitivities methods for solving the sensitivity equations are discussed a numerical implementation of the methods is validated through several examples it is demonstrated that the design sensitivity coefficients dscs of the quantities of interest in charge transport are obtained accurately and that optimal design problems can be solved efficiently using these dscs

conforming boundary elements in plane elasticity for shape design sensitivity the structural design sensitivity analysis of a two dimensional continuum using conforming continuous boundary elements is investigated implicit differentiation of the discretized boundary integral equations is performed to obtain design sensitivities in an efficient manner by avoiding the factorization of the perturbed matrices a singular formulation of the boundary element method is used implicit differentiation of the boundary integral equations produces terms that contain derivatives of the fundamental solutions employed in the analysis the behaviour of the singularity of these derivatives of the boundary element kernel functions with respect to the design variables is investigated a rigid body motion technique is presented to obtain the singular terms in the resulting sensitivity matrices thus avoiding the problems associated with their numerical integration a formulation for obtaining the design sensitivities of the continua under body forces of the gravitational and centrifugal types is also presented the design sensitivity results are seen to be of the same order of accuracy as the boundary element analysis results numerical data comparing the performance of conforming and non conforming formulations in the calculation of design sensitivities are also presented the accuracy of the present results is demonstrated through comparisons with existing analytical results

axisymmetric thermoelastic shape sensitivity analysis and its application to turbine disc design a general method for shape design sensiti vityi analysis sdsa as applied to an axisymmetric thermoelasticity problem is presented using the material derivative concept and the adjoint variable method the sensitivity of a general functional composed of thermal and mechanical quantities is considered the method for deriving the sensitivity formula is based on standard direct thermal and elastic boundary integral equation formulation it is then applied to obtain explicit formulas for a representative displacement and stress constraint imposed on a sector of the boundary results of numerical implementation are presented for weight minimization of a turbine disc under thermomechanical loading the sensitivities of the displacement and stress constraint calculated by the formulas are compared with those by finite differences optimum shape obtained under the thermomechanical loading is discussed with that under the mechanical loading only clearly showing the practical importance of the sdsa of thermoelastic systems

homotopy analysis method for fully developed mhd micropolar fluid flow between vertical porous plates in this paper the fully developed natural convection of mhd micropolar fluid flow between two vertical porous plates is considered the coupled system of non linear differential equations governing the flow is solved analytically by the homotopy analysis method ham the ham contains an auxiliary parameter which provides us with a simple way to adjust and control the convergence region and rate of convergence of the series solution velocity microrotation and temperature profiles are presented for several values of the hartmann number and the micropolar parameter copyright 2008 john wiley sons ltd

axisymmetric viscoplastic deformation by the boundary element method abstract this paper presents a boundary element formulation and numerical implementation of the problem of small axisymmetric deformation of viscoplastic bodies while the extension from planar to axisymmetric problems can be carried out fairly simply for the finite element method fem this is far from true for the boundary element method bem the primary reason for this fact is that the axisymmetric kernels in the integral equations of the bem contain elliptic functions which cannot be integrated analytically even over boundary elements and internal cells of simple shape thus special methods have to be developed for the efficient and accurate numerical integration of these singular and sensitive kernels over discrete elements the accurate determination of stress rates by differentiation of the displacement rates presents another formidable challenge a successful numerical implementation of the boundary element method with elementwise called the mixed approach or pointwise called the pure bem or bem approach determination of stress rates has been carried out a computer program has been developed for the solution of general axisymmetric viscoplasticity problems comparisons of numerical results from the bem and fem for several illustrative problems are presented and discussed in the paper it is possible to get direct solutions for the simpler class of problems for cylinders of uniform cross section and these solutions are also compared with the bem and fem results for such cases

application of the homotopy analysis method to determine the analytical limit state functions and reliability index for large deflection of a cantilever beam subjected to static co planar loading in this paper the homotopy analysis method ham is applied to obtain the limit state function probability of failure and reliability index based on all stochastic and deterministic variables for a cantilever beam subjected to co planar loading for the first time first it is established that a few iterations in the series expansion are sufficient to obtain highly accurate results and a substantial convergence region after showing the effectiveness of ham two limit state functions are introduced as the maximum deflection in the y direction and maximum allowable stress respectively then the first order reliability method form is employed to obtain reliability index and omission sensitivity factor analytically it is shown that ham is a promising tool to obtain limit state function probability of failure and reliability index analytically for nonlinear problems finally a sensitivity analysis is done to show that which parameters could be considered deterministic or stochastic variables

boundary element shape sensitivity analysis for thermal problems with nonlinear boundary conditions implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solid objects subjected to nonlinear boundary conditions is shown to generate an accurate and economical approach for the computation of shape sensitivities for this class of problems this approach involves the employment of analytical derivatives of boundary element kernel functions with respect to shape design variables a formulation is presented that can consistently account for both temperature dependent convection and radiation boundary conditions several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables a series of nonlinear example problems are presented that have closed form solutions 39 refs

design sensitivity coefficients for elasto viscoplastic problems by boundary element methods this paper is concerned with accurate and efficient determination of design sensitivity coefficients dscs for solid mechanics problems with small strains and rotations but with material non linearities present elasto plastic or elasto viscoplastic problems this approach is based on direct differentiation dda of the relevant derivative boundary element method dbem formulation of the problem analytical differentiation of the dbem equations leads to singular integral equations for the dscs with weakly logarithmically for 2 d singular kernels which are easy to deal with also stress components and their sensitivities are obtained on the boundary of a body with great accuracy these quantities are typically difficult to obtain accurately from finite element methods fem a computer program for general two dimensional plane strain and plane stress problems has been developed based on the above formulation numerical results are presented for some sample problems and these are compared against direct solutions the agreement between the dbem and direct solutions is excellent for these examples

flaw identification using the boundary element method in this paper a new boundary element formulation is presented for the identification of the location and size of internal flaws in two dimensional structures an introduction to inverse analysis is given with special reference to methods of flaw identification along with a brief review of the optimization methods employed both the standard boundary element and the dual boundary element method are presented with the dual boundary element method proposed as the basis for the new formulation the flaw identification method is presented along with the computation of the boundary displacement and traction derivatives and the specialized analytical integration used for cracked boundaries examples are given to demonstrate the accuracy of the sensitivity values and the performance of flaw location

semianalytical structural sensitivity formulation in boundary elements developpement d une methode semi analytique qui combine la differenciation implicite des equations integrales frontieres discretisees et une perturbation a une variable etude de milieux continus a symetrie axiale et elastiques plans 2d incluant des forces de volume de type gravite et centrifuge l integration numerique d une nouvelle classe de noyaux de sensibilite des solutions fondamentales est evitee et la mise en uvre est facile presentation de resultats numeriques pour l etude de l effet des perturbations dans les variables du modele

a boundary contour formulation for design sensitivity analysis in two dimensional linear elasticity abstract a formulation for computing first order shape design sensitivities in two dimensional 2 d linear elastostatics by the boundary contour method bcm along with a numerical implementation using quadratic boundary elements is presented in this paper here the direct differentiation approach is analytically applied to the appropriate boundary contour equations in order to derive the sensitivities of all the physical quantities displacements tractions and stresses on the boundary as well as those for displacements and stresses inside the body under consideration the nonsingular formulation of the bcm is used for computing the boundary displacements and boundary stresses at off contour regular points a regular boundary point is a point on the boundary where it is locally smooth an off contour point lies inside a boundary element their corresponding sensitivities are obtained in a straightforward manner from the resulting regular sensitivity formulation also the stress sensitivities at the boundary nodes can be recovered easily from the global displacement shape functions described in a cartesian coordinate system finally through three numerical examples for which analytical solutions exist it is shown that the bcm can provide remarkably accurate numerical results for shape sensitivities

design sensitivity coefficients for linear elastic bodies with zones and corners by the derivative boundary element method abstract the subject of this paper is the efficient and accurate determination of design sensitivity coefficients dscs in an elastic solid with zones and corners direct differentiation of the relevant derivative boundary element method dbem formulation of the problem is carried out here corners and zones in a body are treated carefully with conforming elements a numerical implementation of the method is carried out with isoparametric quadratic boundary elements the power of this approach is demonstrated through several numerical examples it is shown that the dscs of the various mechanical quantities of interest are obtained accurately and efficiently in one example even the dsc of the stress at a corner with respect to the corner angle is obtained very accurately by this method

boundary formulations for shape sensitivity of temperature dependent conductivity problems used in concert with the kirchhoff transformation implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solids with temperature dependent thermal conductivity is shown to generate an accurate and economical approach for computation of shape sensitivities for problems with specified temperature and heat flux boundary conditions a linear problem results for both the analysis and sensitivity analysis in problems with either convection or radiation boundary conditions a non linear problem is generated several iterative strategies are presented for the solution of the resulting sets of non linear equations and the computational performances examined in detail multi zone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized non iinear boundary conditions or regions of geometric insensitivity to design variables a series of non linear example problems is presented that have closed form solutions exact anaytical expressions tor the shape sensitivities associated with these problems are developed and these are compared with the sensitivities computed using the boundary element formulation

transient thermoelasticity and other body force effects in boundary element shape sensitivity analysis several new formulations for structural design sensitivity analysis dsa of elastic solids are presented that consistently account for steady and transient thermal loading along with centrifugal and gravity loading the approach employs implicit differentiation of the discretized boundary integral equations and facilitates the production of accurate and efficient computational procedures that obviate the need for matrix factorizations in the dsa step for centrifugal gravity and general thermal loading a new dsa concept employing a particular integral technique is developed for centrifugal gravity and steady thermal effects a surface integration approach is also presented and the two methods compared alternative strategies for modelling the behaviour of temperature distributions of evolving shapes undergoing shape optimization and the ramifications of these strategies in the dsa process are also discussed it is shown that for certain classes of thermoelastic problems shape optimization can be performed without the need to incorporate thermal analysis or dsa into the overall process a thermoelastic surface stress sensitivity analysis formulation is presented that does not require additional numerical integration a new thermoelastic sharp corner traction component consistent sensitivity analysis formulation is also presented this technique is shown to work for any initial stress distribution numerical sensitivity results are presented for many problems with analytical solutions

reanalysis for structural modifications in boundary element responseand design sensitivity analysis a reanalysis technique is presented for obtaining changes in response variables due to changes in design parameters with the boundary element method the approach is considered for static response analysis and design sensitivity analysis two iterative schemes one based on total quantities and another based on incremental quantities are developed numerical results are obtained for analyses using 1 single zone discretization 2 multizone discretization and 3 multizone discretization with condensation

sensitivity analysis for the dynamic response of thermoviscoplastic shells of revolution abstract a computational procedure is presented for evaluating the sensitivity coefficients of the dynamic axisymmetric fully coupled thermoviscoplastic response of shells of revolution the analytical formulation is based on reissner s large deformation shell theory with the effects of large strain transverse shear deformation rotatory inertia and moments turning around the normal to the middle surface included the material model is chosen to be viscoplasticity with strain hardening and thermal hardening and an associated flow rule is used with a von mises effective stress a mixed formulation is used for the shell equations with the fundamental unknowns consisting of six stress resultants three generalized displacements and three velocity components the energy balance equation is solved using a galerkin procedure with the temperature as the fundamental unknown spatial discretization is performed in one dimension meridional direction for the momentum and constitutive equations of the shell and in two dimensions meridional and thickness directions for the energy balance equation the temporal integration is performed by using an explicit central difference scheme leap frog method for the momentum equation a predictor corrector version of the trapezoidal rule is used for the energy balance equation and an explicit scheme consistent with the central difference method is used to integrate the constitutive equations the sensitivity coefficients are evaluated by using a direct differentiation approach numerical results are presented for a spherical cap subjected to step loading the sensitivity coefficients are generated by evaluating the derivatives of the response quantities with respect to the thickness mass density young s modulus two of the material parameters characterizing the viscoplastic response and the three parameters characterizing the thermal response time histories of the response and sensitivity coefficients are presented along with spatial distributions of some of these quantities at selected times

a boundary integral equation method for radiation and scattering of elastic waves in three dimensions etude du rayonnement et de la diffusion d ondes elastiques par des obstacles de forme arbitraire

direct differentiation formulation for boundary element shape sensitivity analysis of axisymmetric elastic solids abstract an efficient direct differentiation method by continuum approach is presented for the shape design sensitivity analysis of axisymmetric elastic solids the method is purely based on the axisymmetric boundary integral equation formulation a new boundary integral equation for sensitivity analysis is derived by taking material derivative to the same integral identity that was used in the adjoint method as sensitivities in terms of the shape design variables are directly calculated by solving the new bie the singular boundary condition which may arise in the adjoint method is avoided in the present direct method to validate the theoretical formulation numerical implementation is done for three examples for a hollow disk and a thick walled cylinder problem with analytic solution the sensitivities by present method are compared with analytic sensitivities for an example of a spherical vessel being rather practical the sensitivities are compared with those by finite differences

a boundary integral formulation for complex three dimensional geometries a new boundary integral formulation is proposed to analyse the heat transfer in complex three dimensional geometries one example of such geometry is the die sets in the injection moulding process networks of cooling conduits within the mould and the closely spaced die surfaces require special attention both in formulation and numerical treatment of the integral equations the proposed formulation couples the boundary formula the gradient of the boundary formula and the exterior formula the derivation of the integral equations is presented here along with an efficient method for integration of some of the kernels in these equations and a semi analytical procedure for the integration of the highly singular integrands which result from differentiating the boundary formula although the techniques introduced here are applied to a particular problem in heat transfer their potential application is much broader

boundary element implicit differentiation equations for design sensitivities of axisymmetric structures abstract design sensitivity analysis of axisymmetric elastic media is formulated using boundary elements the kernels for sensitivity matrices are obtained through implicit differentiation of the corresponding boundary element elasticity kernels the singular terms are obtained by applying the boundary displacements and tractions and their respective sensitivities for the rigid body motion mode and the inflation mode the equations for the recovery of sensitivities of axisymmetric boundary stresses are presented as a check on accuracy the approach is applied to a series of examples for which analytical elasticity solutions are available the predictions for both displacement and stress sensitivities are accurate additional examples are provided to demonstrate the versatility of the present approach