Chirality in isotropic linear gradient elasticity

Conservation Laws in Elasticity II. Linear Homogeneous Isotropic Elastostatics

Gradient schemes for linear and non-linear elasticity equations

The Gradient Scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the Gradient Scheme framework can be adapted to elasticity equations, and provides error estimates for linear elasticity and convergence results for non-linear elasticity. We also establish that several classical and modern numeri...

Shape Gradient Computation in Isogeometric Analysis for Linear Elasticity

The transfer of geometrical data from CAD (Computer Aided Design) to FEA (Finite-Element Analysis) is a bottleneck of automated design optimization procedures, yielding a loss of accuracy and cumbersome software couplings. Isogeometric analysis methods propose a new paradigm that allows to overcome these difficulties by using a unique geometrical representation that yields a direct relationship...

Preconditioned Conjugate Gradient Methods for Three Dimensional Linear Elasticity

Finite element modelling of three dimensional elasticity problems gives rise to large sparse matrices. Various preconditioning methods are developed for use in preconditioned conjugate gradient iterative solution techniques. Incomplete factorizations based on levels of fill, drop tolerance, and a two level hierarchical basis are developed. Various techniques for ensuring that the incomplete fac...

Two robust nonconforming H-elements for linear strain gradient elasticity

B Pingbing Ming [email protected] Hongliang Li [email protected] Zhong-ci Shi [email protected] 1 Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621900, China 2 The State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, No. 55, Zhong-Guan-Cun East Road, Beijing 100190, China...