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SUMMARYThe first (for the given class of problems) results of solving non-stationary plane problems of nonsimultaneous origination of holes and inclusions in a preliminary loaded solid with initial finite strains are presented and discussed. It is taken into account that the origination of a hole or an inclusion produces additional finite deformations (at least, at the vicinity of the hole) superimposed 'physically' on the finite initial ones. The problem is solved using the theory of repeated superposition of large deformations. It is supposed that the shape of stress concentrators is given at the moment of their origination.Calculations were made with the use of the specialized computer package 'Superposition' based on finite-element method. Stress fields are presented at different times. The change of maximal stresses in time is also presented. Copyright q 2008 John Wiley & Sons, Ltd. The first (for the given class of problems) results of solving non-stationary plane problems of non-simultaneous origination of holes and inclusions in a preliminary loaded solid with initial finite strains are presented and discussed.The solid's material is described by the Murnaghan potential. It is taken into account that the origination of holes and inclusions produces additional finite deformations (at least, at the vicinity of the hole) superimposed 'physically' on the finite initial ones.The problem is solved using the theory of repeated superposition of large deformations developed by Levin [1]. The given theory allows one to formulate and to solve problems for the case of finite strains when boundaries and boundary conditions are changed repeatedly. Moreover, this theory allows one to take into account the change of connectedness of a solid's domain and also the change of material properties of a part of the solid under loading.

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Modern high-performance computing systems allow us to explore and implement new technologies and mathematical modeling algorithms into industrial software systems of engineering analysis. For a long time the finite element method (FEM) was considered as the basic approach to mathematical simulation of elasticity theory problems; it provided the problems solution within an engineering error. However, modern high-tech equipment allows us to implement design solutions with a high enough accuracy, which requires more sophisticated approaches within the mathematical simulation of elasticity problems in industrial packages of engineering analysis. One of such approaches is the spectral element method (SEM). The implementation of SEM in a CAE system for the solution of elasticity problems is considered. An important feature of the proposed variant of SEM implementation is a support of hybrid curvilinear meshes. The main advantages of SEM over the FEM are discussed. The shape functions for different classes of spectral elements are written. Some results of computations are given for model problems that have analytical solutions. The results show the better accuracy of SEM in comparison with FEM for the same meshes.