In this paper an application of the additive multilevel iteration method to parallel solving of large{scale linear elasticity problems is considered. The results are derived in the framework of the hierarchical basis nite{element discretization deened on a tensor product ^ T (i) xyz = ^ T (i) xy ^ T z of one{dimensional grid ^ T z and a sequence of nested triangula-tions ^ T (i) xy. The algorit...

In this paper, the Trefftz collocation method is applied to solve the inverse Cauchy problem of anisotropic elasticity, wherein both tractions as well as displacements are prescribed at a small part of the boundary of an arbitrary simply/multiply connected anisotropic elastic domain. The Stroh formalism is used to construct the Trefftz basis functions. Negative and positive power series are use...

A numerical method called the Boundary Walk Method (BWM) is used to solve problems in two-dimensional potential theory and linear elasticity in multiply connected domains. The BWM is a local method in the sense that it directly gives the solution at the point of interest. It is based on a global integral representation of the unknown function in the form of a potential, followed by evaluating t...

Abstract In this work, the Mellin transform method was used to obtain solutions for the stress field components in two dimensional (2D) elasticity problems in terms of plane polar coordinates. the Mellin transformation was applied to the biharmonic stress compatibility equation expressed in terms of the Airy stress potential function, and the boundary value problem transformed to an algebraic  ...

In this paper, topology optimization is utilized for damage detection in three dimensional elasticity problems. In addition, two mode expansion techniques are used to derive unknown modal data from measured data identified by installed sensors. Damages in the model are assumed as reduction of mass and stiffness in the discretized finite elements. The Solid Isotropic Material with Penalization (...

A finite element method is considered for dealing with nearly incompressible material. In the case of large deformations the nonlinear character of the volumetric contribution has to be taken into account. The proposed mixed method avoids volumetric locking also in this case and is robust for λ→∞ (with λ being the well-known Lamé constant). Error estimates for the L∞-norm are crucial in the con...

In this paper we discuss the implementation of parallel multigrid methods on unstructured locally refined meshes for 2D linear elasticity calculations. The problem of rebalancing the workload of the processors during execution of the program is discussed in detail and a load balancing algorithm suited for hierarchical meshes is proposed. For large problems the efficiency per multigrid iteration...

Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techn...

The peak cap stress (PCS) amplitude is recognized as a biomechanical predictor of vulnerable plaque (VP) rupture. However, quantifying PCS in vivo remains a challenge since the stress depends on the plaque mechanical properties. In response, an iterative material finite element (FE) elasticity reconstruction method using strain measurements has been implemented for the solution of these inverse...

A new fast multipole formulation for the hypersingular BIE (HBIE) for 2D elasticity is presented in this paper based on a complex-variable representation of the kernels, similar to the formulation developed earlier for the conventional BIE (CBIE). A dual BIE formulation using a linear combination of the developed CBIE and HBIE is applied to analyze multi-domain problems with thin inclusions or ...