The method of fundamental solutions for the Cauchy problem in two-dimensional linear elasticity

From MaRDI portal
Publication:557325

DOI10.1016/j.ijsolstr.2004.02.009zbMath1071.74055OpenAlexW1968354363MaRDI QIDQ557325

Daniel Lesnic, Liviu Marin

Publication date: 23 June 2005

Published in: International Journal of Solids and Structures (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ijsolstr.2004.02.009




Related Items

A meshless method based on the fundamental solution and radial basis function for solving an inverse heat conduction problemThe fundamental solution of mindlin plates resting on an elastic foundation in the Laplace domain and its applicationsMatrix decomposition MFS algorithms for elasticity and thermo-elasticity problems in axisymmetric domainsAn energy error-based method for the resolution of the Cauchy problem in 3D linear elasticitySolution of nonlinear Cauchy problem for hyperelastic solidsA new approximate method for an inverse time-dependent heat source problem using fundamental solutions and RBFsA matrix decomposition MFS algorithm for certain linear elasticity problemsMethod of fundamental solutions and high order algorithm to solve nonlinear elastic problemsA meshless method for solving 1D time-dependent heat source problemIdentification of boundary conditions by solving Cauchy problem in linear elasticity with material uncertaintiesThe method of fundamental solutions for the inverse space-dependent heat source problemInverse heat conduction problem in two-dimensional anisotropic mediumModified method of fundamental solutions for the Cauchy problem connected with the Laplace equationConvergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticityA meshless method for the Cauchy problem in linear elastodynamicsAn optimization approach for the Cauchy problem in linear elasticityBoundary reconstruction in two-dimensional steady state anisotropic heat conduction using a regularized meshless methodRegularized method of fundamental solutions for boundary identification in two-dimensional isotropic linear elasticityRelaxation procedures for an iterative MFS algorithm for the stable reconstruction of elastic fields from Cauchy data in two-dimensional isotropic linear elasticityFading regularization MFS algorithm for the Cauchy problem associated with the two-dimensional Stokes equationsIdentification of force loadings on the inner circumference of a finite‐length elastic cylinderThe minimal error method for the Cauchy problem in linear elasticity. Numerical implementation for two-dimensional homogeneous isotropic linear elasticityThe MFS for numerical boundary identification in two-dimensional harmonic problemsRelaxation procedures for an iterative MFS algorithm for two-dimensional steady-state isotropic heat conduction Cauchy problemsCombining MFS and PGD methods to solve transient heat equationA meshless method for the stable solution of singular inverse problems for two-dimensional Helmholtz-type equationsInverse source identification by Green's functionThe method of fundamental solutions for the inverse heat source problemThe fundamental solution of Mindlin plates with damping in the Laplace domain and its applicationsOn the determination of missing boundary data for solids with nonlinear material behaviors, using displacement fields measured on a part of their boundariesInverse fracture problems in piezoelectric solids by local integral equation methodAn overview of the method of fundamental solutions -- solvability, uniqueness, convergence, and stabilityA relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticityAn iterative method for the Cauchy problem in linear elasticity with fading regularization effectA method of fundamental solutions for inverse heat conduction problems in an anisotropic mediumAn alternating iterative algorithm for the Cauchy problem in anisotropic elasticityAn integral equations method combined minimum norm solution for 3D elastostatics Cauchy problemNonlinear Cauchy problem and identification in contact mechanics: a solving method based on Bregman-gapApplication of the Trefftz method, on the basis of Stroh formalism, to solve the inverse Cauchy problems of anisotropic elasticity in multiply connected domainsBoundary element methods for boundary condition inverse problems in elasticity using PCGM and CGM regularizationThe method of fundamental solutions and condition number analysis for inverse problems of Laplace equationExponential basis functions in solution of static and time harmonic elastic problems in a meshless styleDetermination of elastic resonance frequencies and eigenmodes using the method of fundamental solutionsNon-iterative regularized MFS solution of inverse boundary value problems in linear elasticity: a numerical studyAn invariant method of fundamental solutions for the Cauchy problem in two-dimensional isotropic linear elasticityOn a fixed point study of an inverse problem governed by Stokes equationExtending the method of fundamental solutions to non-homogeneous elastic wave problemsAnalysis of Lavrentiev-finite element methods for data completion problemsA survey of applications of the MFS to inverse problemsAn alternating iterative MFS algorithm for the Cauchy problem for the modified Helmholtz equationA numerical study of the SVD–MFS solution of inverse boundary value problems in two‐dimensional steady‐state linear thermoelasticityStress intensity factor computation using the method of fundamental solutionsWeighted reproducing kernel collocation method based on error analysis for solving inverse elasticity problemsOn the Determination of a Robin Boundary Coefficient in an Elastic Cavity Using the MFSThe method of fundamental solutions for two-dimensional elasticity problems based on the Airy stress functionSimultaneous determination for a space-dependent heat source and the initial data by the MFSNumerical identification for impedance coefficient by a MFS-based optimization methodMathematical foundation of the MFS for certain elliptic systems in linear elasticityFull Discretization of Cauchy's Problem by Lavrentiev--Finite Element MethodA numerical study on the solution of the Cauchy problem in elasticityThe method of fundamental solution for the inverse source problem for the space-fractional diffusion equationThe method of fundamental solutions for inverse 2D Stokes problemsSimultaneous determination of a time-dependent heat source and the initial temperature in an inverse heat conduction problemA meshless method for solving the Cauchy problem in three-dimensional elastostatics