a mixed variational method for linear coupled thermoelastic analysis abstract a variational method for linear coupled quasi static thermoelastic analysis is presented the variational support is a statement in terms of displacement temperature stress and heat flux the statement is based on the hybrid stress formulation for the elastic part and on the mixed flux temperature formulation for the thermal one and includes the rate dependent terms of the energy balance equations and the initial condition a finite element model for the semidiscrete analysis is developed within this variational framework and a guideline for implementing a family of thermoelastic finite elements is given some test cases enlighten the effectiveness and reliability of the approach proposed

variational and projection methods for the volume constraint in finite deformation elasto plasticity this paper focuses on the treatment of volume constraints which in the context of elasto plasticity typically arise as a result of assuming volume preserving plastic flow projection methods based on the modification of the discrete gradient operator b often proposed on an ad hoc basis are systematically obtained in the variational context furnished by a three field hu washizu principle the fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume preserving and dilatational parts without relying on rate forms of the weak form of momentum balance this approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient and enables one to exactly enforce the condition of volume preserving plastic flow within the framework proposed in this paper rate forms and incrementally objective algorithms are entirely bypassed

recent trends in ale formulation and its applications in solid mechanics this paper presents a complete derivation and implementation of the arbitrary lagrangian eulerian ale formulation for the simulation of nonlinear static and dynamic problems in solid mechanics the ale equations are presented using a fully coupled implicit approach full expression for the ale virtual work equations and finite element matrices are given the matrix equations are presented in a level of details that facilitates straightforward implementation time integration relations for the dynamic equations are also derived special techniques are presented to adapt the formulation for simulating crack propagation problems several applications in the areas of metal forming metal cutting and crack propagation are solved and presented

a mixed finite element for the analysis of large inelastic strains a 4 node element with 1 integration point is developed for the analysis of elastoplastic large strains it is based on the hu washizu principle and uses a co rotational formulation special care is taken to avoid spurious zero energy modes and incompressibility locking this element successfully passes the large strain patch test it proves to be accurate and computationally very cheap

enhanced local maximum entropy approximation for stable meshfree simulations abstract we introduce an improved meshfree approximation scheme which is based on the local maximum entropy strategy as a compromise between shape function locality and entropy in an information theoretical sense the improved version is specifically designed for severe finite deformation and offers significantly enhanced stability as opposed to the original formulation this is achieved by i formulating the quasistatic mechanical boundary value problem in a suitable updated lagrangian setting ii introducing anisotropy in the shape function support to accommodate directional variations in nodal spacing with increasing deformation and eliminate tensile instability iii spatially bounding and evolving shape function support to restrict the domain of influence and increase efficiency iv truncating shape functions at interfaces in order to stably represent multi component systems like composites or polycrystals the new scheme is applied to benchmark problems of severe elastic and elastoplastic deformation that demonstrate its performance both in terms of accuracy as compared to exact solutions and where applicable finite element simulations and efficiency importantly the presented formulation overcomes the classical tensile instability found in most meshfree interpolation schemes as shown for stable simulations of e g the inhomogeneous extension of a hyperelastic block up to 100 or the torsion of a hyperelastic cube by 200 both in an updated lagrangian setting and without the need for remeshing

an updated lagrangian finite element sensitivity analysis of large deformations using quadrilateral elements a continuum parameter and shape sensitivity analysis is presented for metal forming processes using the finite element method the sensitivity problem is posed in a novel updated lagrangian framework as suitable for very large deformations when remeshing operations are performed during the analysis in addition to exploring the issue of transfer of variables between meshes for finite deformation analysis the complex problem of transfer of design sensitivities derivatives between meshes for large deformation inelastic analyses is also discussed a method is proposed that is shown to give accurate estimates of design sensitivities when remeshing operations are performed during the analysis sensitivity analysis for the consistent finite element treatment of near incompressibility within the context of the assumed strain methods is also proposed in particular the performance of four noded quadrilateral elements for the sensitivity analysis of large deformations is studied the results of the continuum sensitivity analysis are validated by a comparison with those obtained by a finite difference approximation i e using the solution of a perturbed deformation problem the effectiveness of the method is demonstrated by applications in the design optimization of metal forming processes copyright 2001 john wiley sons ltd

dilation method and smoothing effects of solutions to the benjamin ono equation in this paper we study smoothing effects of solutions to the benjamin ono equation where h is the hilbcrt transform defined by we prove that if h 2 and x x 4 then the solution u of bo belongs to where

a particle level set based sharp interface cartesian grid method for impact penetration and void collapse an eulerian sharp interface cartesian grid method is developed for the numerical simulation of the response of materials to impact shocks and detonations the mass momentum and energy equations are solved along with evolution equations for deviatoric stresses and equivalent plastic strain these equations are cast in eulerian conservation law form the mie gruneisen equation of state is used to obtain pressure and the material is modeled as a johnson cook solid the eno scheme is employed to capture shocks in combination with a hybrid particle level set technique to evolve sharp immersed boundaries the numerical technique is able to handle collisions between multiple materials and can accurately compute the dynamics of the immersed boundaries results of calculations for axisymmetric taylor bar impact and penetration of a tungsten rod into steel plate show good agreement with moving finite element solutions and experimental results qualitative agreement with theory is shown for the void collapse phenomenon in an impacted material containing a spherical void

geometrically non linear enhanced strain mixed methods and the method of incompatible modes a class of assumed strain mixed finite element methods for fully non linear problems in solid mechanics is presented which when restricted to geometrically linear problems encompasses the classical method of incompatible modes as a particular case the method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part formulated in the context of a three field variational formulation the resulting class of mixed methods provides a possible extension to the non linear regime of well known incompatible mode formulations in addition this class of methods includes non linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements the good performance of the proposed methodology is illustrated in a number of simulations including 2 d 3 d and axisymmetric finite deformation problems in elasticity and elastoplasticity remarkably these methods appear to be specially well suited for problems involving localization of the deformation as illustrated in several numerical examples

regularity of solutions to nonlinear dispersive equations on considere le probleme de cauchy pour les equations dispersives non lineaires de la forme t u ip d u f u x r n t u x 0 u 0 x

an eulerian particle level set method for compressible deforming solids with arbitrary eos in this study an eulerian finite volume method is developed for the numerical simulation of elastic plastic response of compressible solid materials with arbitrary equation of state eos under impact loading the governing equations of mass momentum and energy along with evolution equations for deviatoric stresses are solved in eulerian conservation law form since the position of material boundaries is determined implicitly by eulerian schemes the solution procedure is split into two separate subproblems which are solved sequentially at each time step first the conserved variables are evolved in time with appropriate boundary conditions at the material interfaces in the present work a fourth order central weighted essentially non oscillatory shock capturing method that was developed for gas dynamics has been extended to high strain rate solids problems in this method fluxes are determined on a staggered grid at places where solution is smooth as a result the method does not rely on the solution of riemann problems but enjoys the flexibility of using any type of eos boundary conditions at material interfaces are also treated by a special ghost cell approach then in the second subproblem the position of material interfaces is advanced to the new time using a particle level set method a fifth order godunov type central scheme is used to solve the hamilton jacobi equation of level sets in two space dimensions the capabilities of the proposed method are evaluated at the end by comparing numerical results with the experimental results and the reported benchmark solutions for the taylor rod impact spherical groove jetting and void collapse problems copyright 2009 john wiley sons ltd

unified and mixed formulation of the 4 node quadrilateral elements by assumed strain method application to thermomechanical problems in this paper a class of assumed strain mixed finite element methods based on the hu washizu variational principle is presented special care is taken to avoid hourglass modes and shear locking as well as volumetric locking an unified framework for the 4 node quadrilateral solid and thermal as well as thermomechanical coupling elements with uniform reduced integration uri and selective numerical integration si schemes is developed the approach is simply implemented by a small change of the standard technique and is applicable to arbitrary non linear constitutive laws including isotropic and anisotropic material behaviours the implementation of the proposed si elements is straightforward while the development of the proposed uri elements requires anti hourglass stresses which are evaluated by classical constitutive equations several numerical examples are given to demonstrate the performance of the suggested formulation including static dynamic mechanical problems heat conduction and thermomechanical problems

absorption compensation method by l1 norm regularization abstractabsorption in subsurface media greatly reduces the resolution of seismic data absorption not only dissipates the high frequency components of the wave but it also distorts the seismic wavelet the inverse q filtering method is an effective method to correct the attenuation and dispersion of the seismic wave we evaluated an absorption compensation method based on l1 norm regularization forward modeling in the absorption medium is described by a fredholm integral equation in the time domain and the absorption compensation comes down to solving the fredholm integral equation the solutions of the fredholm integral equation are extremely unstable generally l2 norm regularization can be used to seek stable solutions of the fredholm integral equation but it makes the solutions smooth and reduces the resolution of seismic data we used l1 norm regularization to overcome instability of solving the integral equation it makes the solutions have a higher resolution than l2 norm regularization the i

numerical solution of a parabolic system with coupled nonlinear boundary conditions a numerical technique has been developed to solve a system that consists of m linear parabolic differential equations with coupled nonlinear boundary conditions such a system may represent chemical reactions chemical lasers and diffusion problems an implicit finite difference scheme is adopted to discretize the problem and the resulting system of equations is solved by a novel technique that is a modification of the cyclic odd even reduction and factorization corf algorithm at each time level the system of equations is first reduced to m nonlinear algebraic equations that involve only the m unknown grid points on the nonlinear boundary newton s method is used to determine these m unknowns and the corresponding jacobian matrix can be computed and updated easily after convergence is achieved the remaining unknowns are solved directly the efficiency of this technique is illustrated by the numerical computations of two examples previously solved by the cubic spline galerkin method

a fractal patch test element consistency is generally checked using the patch test on an element patch of finite size this condition may in certain cases be too restrictive and disqualifies elements that appear to be convergent a method termed fractal patch test is presented in which the patch size is maintained constant while the distorted mesh is refined examples are given for four node quadrilateral elements used in plane stress and strain analysis and for plate bending elements

a stabilization procedure for the quadrilateral plate element with one point quadrature a stabilization procedure is developed for controlling the kinematic modes of the four node bilinear quadrilateral element when single point quadrature is used these kinematic modes manifest themselves by spatial oscillations or singularity of the total stiffness in this stabilization procedure additional generalized strains are defined which are activated by the kinematic modes these generalized modes are furthermore not activated by rigid body motions regardless of the shape of the quadrilateral by using a scaling law developed in an earlier paper the stabilization parameters are defined so they do not adversely affect the element s performance several problems which are subject to kinematic modes are presented to illustrate the performance of this stabilization procedure for linear problems

treatment of internal constraints by mixed finite element methods unification of concepts a general method to generate assumed stress and strain fields within the context of mixed finite element methods is presented the assumed fields are constructed in such a way that internal constraints are satisfied a priori consequently the locking behaviour commonly observed in finite element solutions of problems with internal constraints is avoided to this end the assumed stress and strain fields are constructed to satisfy a priori the homogeneous part of the equilibrium equations thus avoiding fraeijs de veubeke s limitation principle results obtained using the proposed methodology on a nearly incompressible plane strain problem and thin plate application using a shear deformable theory are indicated

finite element stabilization matrices a unification approach abstract in this paper we show that the stabilization vector can be obtained naturally by taking the partial derivatives with respect to the natural coordinates hence the components of the strains and stresses can be expressed in terms of a set of orthogonal coordinates with these definitions of stresses and strains a general form of the finite element stabilization matrices is then constructed for underintegrated irregular shape and anisotropic elements the explicit expressions of the stabilization matrices for the 4 9 and 8 node laplace and continuum elements and the 4 node plate element are then derived from the general form these are sufficiently general for the developments herein the generalization of the stabilization matrices concept to nonlinear problems which usually require the numerical integration of a fairly general class of nonlinear finite deformation constitutive equations is also presented the computer implementation aspects and numerical evaluation of these stabilized elements are also considered numerical tests confirm the stability and accuracy characteristics of the resulting elements in particular the numerical experiments reported here also show that the rates of convergence in the l2 norm and in the energy norm agree well with the expected convergence rates

efficient linear and nonlinear heat conduction with a quadrilateral element a method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one point quadrature the stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter it is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values in fact the values 3 2 and 1 for the normalized stabilization parameter lead to the 5 point finite difference 9 point finite difference and fully integrated finite element operators respectively for rectangular meshes numerical experiments reported here show that the three have identical rates of convergence in the l2 norm eigenvalues of the element matrices which are needed for stability limits are also given numerical applications are used to show that the method yields accurate solutions with large increases in efficiency particularly in nonlinear problems

weighted sobolev spaces and rapidly decreasing solutions of some nonlinear dispersive wave equations where d is a positive integer a is a d dimensional laplacian and the subscripts x t denote partial differentiations the initial value problems for 1 i 1 3 require the asymptotic conditions as x tends to infinity and one must specify spaces of functions satisfying the desired asymptotic conditions the usual choices of spaces are the sobolev spaces z p well posedness in hs of the initial value problems for 1 1 1 3 was established by many authors 3 5 8 12 181 it is of interest to know that eqs l l 1 3 have solutions decreasing faster than hs convergence as x tends to infinity in particular solutions in the schwartz spaces s for each t provided that their initial data are in s this is motivated by tanaka s result for the korteweg de vries equation 131 which establishes the existence of s solutions by the inverse scattering techniques and by the fact that eqs l l 1 3 have travelling solutions in s solitary waves which may play an important role of asymptotic behavior of solutions as t tends to infinity

a uniform strain hexahedron and quadrilateral with orthogonal hourglass control the treatment of zero energy modes which arise due to one point integration of first order isoparametric finite elements is addressed a method for precisely isolating these modes for arbitrary geometry is developed two hourglass control schemes viscous and elastic are presented and examined in addition a convenient one point integration scheme which analytically integrates the element volume and uniform strain modes is presented

on the suppression of zero energy deformation modes based on the hellinger reissner principle and the deformation energy due to assumed stresses and displacements the problem of the kinematic deformation modes in assumed stress hybrid mixed finite elements has been examined basic schemes are developed for the choice of assumed stress terms that will suppress all kinematic deformation modes quadrilateral membrane and axisymmetric elements and three dimensional hexahedral elements are used to illustrate the suggested procedure

hourglass control in linear and nonlinear problems abstract mesh stabilization techniques for controlling the hourglass modes in under integrated hexahedral and quadrilateral elements are described it is shown that the orthogonal hourglass techniques previously developed can be obtained from simple requirements that insure the consistency of the finite element equations in the sense that the gradients of linear fields are evaluated correctly it is also shown that this leads to an hourglass control that satisfies the patch test the nature of the parameters which relate the generalized stresses and strains for controlling hourglass modes is examined by means of a mixed variational principle and some guidelines for their selection are discussed finally effective means of implementing these hourglass procedure in computer codes are described applications to both the laplace equation and the equations of solid mechanics in 2 and 3 dimensions are considered

seismic absorption compensation a least squares inverse scheme the problem of instability plagues conventional inverse q filtering we formulate the deabsorption problem as an inverse problem in terms of least squares and impose regularization by means of bayes theorem the solution is iterative and nonparametric and returns a reflectivity that has been constrained to be sparse the inverse scheme is tested on both synthetic and real data and the results obtained demonstrate the viability of the approach

quadrilateral elements for the solution of elasto plastic finite strain problems in this paper two plane strain quadrilateral elements with two and four variables are proposed these elements are applied to the analysis of finite strain elasto plastic problems the elements are based on the enhanced strain and b bar methodologies and possess a stabilizing term the pressure and dilatation fields are assumed to be constant in each element s domain and the deformation gradient is enriched with additional variables as in the enhanced strain methodology the formulation is deduced from a four field functional based on the imposition of two constraints annulment of the enhanced part of the deformation gradient and the relation between the assumed dilatation and the deformation gradient determinant the discretized form of equilibrium is presented and the analytical linearization is deduced to ensure the asymptotically quadratic rate of convergence in the newton raphson method the proposed formulation for the enhanced terms is carried out in the isoparametric domain and does not need the usually adopted procedure of evaluating the jacobian matrix in the centre of the element the elements are very effective for the particular class of problems analysed and do not present any locking or instability tendencies as illustrated by various representative examples copyright 2001 john wiley sons ltd

optimal transportation meshfree approximation schemes for fluid and plastic flows we develop an optimal transportation meshfree otm method for simulating general solid and fluid flows including fluid structure interaction the method combines concepts from optimal transportation theory with material point sampling and max ent meshfree interpolation the proposed otm method generalizes the benamou brenier differential formulation of optimal mass transportation problems to problems including arbitrary geometries and constitutive behavior the otm method enforces mass transport and essential boundary conditions exactly and is free from tension instabilities the otm method exactly conserves linear and angular momentum and its convergence characteristics are verified in standard benchmark problems we illustrate the range and scope of the method by means of two examples of application the bouncing of a gas filled balloon off a rigid wall and the classical taylor anvil benchmark test extended to the hypervelocity range

similarity and the inverse q filter the pareto levy stretch the seismic impulse response of a constant q attenuating material has the same mathematical form as the density function for the pareto levy probability law since this law is stable it follows that the seismic pulse is closed under convolution this means that if the distance from the source x is the sum of two distances x x1 x2 then the pulse at x is the convolution of the pulse at x1 with the one at x2 its amplitude is proportional to x1 where the parameter 0 1 depends only on q with 1 corresponding to a loss free material q as the pulse loses amplitude it stretches along the time axis so that its area is preserved this scaling between time and distance is illustrated by the stationary phase approximation for the constant q pulse the approximation becomes increasingly more accurate for small values of q until q 1 2 where it is exact it becomes the solution to the heat equation log stretch inverse q filtering of seismic data is performed by logarithmically stretching the time ax

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

rational approach for assumed stress finite elements a new method for the formulation of hybrid elements by the hellinger reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element the equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co ordinates the resulting element possesses all the ideal qualities i e it is invariant it is less sensitive to geometric distortion it contains a minimum number of stress parameters and it provides accurate stress calculations for the formulation of a 4 node plane stress element a small perturbation method is used to determine the equilibrium constraint equations the element has been proved to be always rank sufficient

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

analysis of hourglass instabilities and control in underintegrated finite element methods belytschko et al 1981 1984 has developed stabilization methods for the treatment of underintegrated fem problems these methods involve the computation of an underintegrated stiffness matrix which is rank deficient and the addition of a stabilization matrix which effectively eliminates the spurious modes an attempt is presently made to give this a priori stabilization method a mathematical means of support attention is also given to an a posteriority stabilization method for hourglass control in which an approximate solution of the underintegrated system is obtained and then subjected to a special projection in order to eliminate the hourglass modes a proof is obtained for the convergence of this stabilized underintegrated approximation to the exact solution of a model problem at almost the same rate as the mesh is refined as the fully integrated solutions