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Antonio Signorini and the proto-history of the non-linear theory of elasticity
Antonio Signorini’s contribution to the constitutive theory of non-linear elasticity is reconstructed and analyzed. Some uninformed opinions...
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Live load matrix recovery from scattering data in linear elasticity
We study the numerical approximation of the inverse scattering problem in the two-dimensional homogeneous isotropic linear elasticity with an unknown...
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Computational algorithms for solving optimal control in linear elasticity
This paper mainly investigates linear elastic optimal control problems with two constraints: distributed load control and boundary load control. The...
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Two-Term Spectral Asymptotics in Linear Elasticity
We establish the two-term spectral asymptotics for boundary value problems of linear elasticity on a smooth compact Riemannian manifold of arbitrary...
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Shape optimization for composite materials in linear elasticity
This article is devoted to the optimal design of the microstructure in composite materials, which are governed by the equations of linear elasticity....
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Topology Optimization in Linear Elasticity, Plasticity and Fracture Mechanics
This chapter presents the theoretical and the numerical study of shape and topology optimization for linear elasticity, plasticity and fracture using...
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An adaptive algorithm for Steklov eigenvalues of the Lamé operator in linear elasticity
The Steklov eigenvalues of the Lamé operator arise from the analysis of surface waves and vibration modes in a linearly elastic structure. In this...
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A mixed virtual element method for nearly incompressible linear elasticity equations
A new virtual element method is proposed for numerically solving the nearly incompressible linear elasticity problem which involves a Lamé...
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Worked Out Problem 2: A Linear Elasticity Problem on a Square
In this chapter, we consider a vector elliptic PDE modeling a parametric linear elasticity problem in a two-dimensional heterogeneous domain. The aim...
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Defining Equations of the Anisotropic Moment Linear Theory of Elasticity and the Two-Dimensional Problem of Pure Shear with Constrained Rotation
AbstractThe paper presents the equations of the linear moment theory of elasticity for the case of arbitrary anisotropy of material tensors of the...
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Penalty-Free Any-Order Weak Galerkin FEMs for Linear Elasticity on Quadrilateral Meshes
This paper develops a family of new weak Galerkin (WG) finite element methods (FEMs) for solving linear elasticity in the primal formulation. For a...
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An Interface/Boundary-Unfitted EXtended HDG Method for Linear Elasticity Problems
An interface/boundary-unfitted eXtended hybridizable discontinuous Galerkin (X-HDG) method of arbitrary order is proposed for linear elasticity...
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Some Remarks on the Virtual Element Method for the Linear Elasticity Problem in Mixed Form
The Virtual Element Methods for the linear elasticity problems are considered, in the framework of the Hellinger–Reissner variational principle....
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A Posteriori Analysis for a Mixed FEM Discretization of the Linear Elasticity Spectral Problem
In this paper we analyze a posteriori error estimates for a mixed formulation of the linear elasticity eigenvalue problem. A posteriori estimators...
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Worked Out Problem 11: A Linear Elasticity Application on a Beam Bridge
In this chapter, we consider a vector elliptic PDE modeling a linear elasticity problem for bridge designing in a two-dimensional and geometrically...
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Worked Out Problem 10: An Idealized Contact Problem in Linear Elasticity with Friction
In this chapter, we consider a vector elliptic PDE modeling a contact problem in linear elasticity with friction in a two-dimensional and...
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An efficient computation of the inverse of the single layer matrix for the resolution of the linear elasticity problem in BEM
In this paper, we describe and analyze fast procedures for numerical resolution of Dirichlet and mixed boundary value problems in linear elasticity,...
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Linear elasticity
The present chapter is concerned with the linear elasticity equations where the main tool to establish coercivity is Korn’s inequality. We consider...
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Identification of Cavities and Inclusions in Linear Elasticity with a Phase-Field Approach
In this paper we deal with the inverse problem of determining cavities and inclusions embedded in a linear elastic isotropic medium from boundary...
