Numerical Solution Of Three-dimensional Problems Research Articles

Cosserat point element (CPE) for finite deformation of orthotropic elastic materials

An eight node brick Cosserat point element (CPE) has been developed for the numerical solution of three-dimensional problems of hyperelastic nonlinear orthotropic elastic materials. In the Cosserat approach, a strain energy function for the CPE is proposed which satisfies restrictions due to a nonlinear form of the patch test. Part of the strain energy of the CPE is characterized by a three-dimensional strain energy function that depends on physically based nonlinear orthotropic invariants. Special attention has been focused on developing closed form expressions for constitutive coefficients in another part of the strain energy that characterizes the response to inhomogeneous deformations appropriate for orthotropic material response. A number of example problems are presented which demonstrate that the CPE is a robust user friendly element for finite deformations of orthotropic elastic materials, which does not exhibit unphysical locking or hourglassing for thin structures or nearly incompressible materials.

Numerical solution of three-dimensional problems of filtration consolidation with regard for the influence of technogenic factors by the method of radial basis functions

We use a meshless method to find an approximate solution of the problem that describes a mathematical model of the filtration consolidation process in a three-dimensional domain. It is based on the collocation method using radial basis functions. The performed numerical experiments testify to the efficiency of the proposed approach.

Use of a Combined Grid for Numerical Solution of Three-Dimensional Problems of Hydrodynamics and Heat Transfer by the Control-Volume Technique

The authors suggest a version of the control-volume technique that uses a single common grid at whose points velocity components and other dependent variables are calculated. It is shown that the suggested rocedure does not admit perception of a “checkered” pressure field as homogeneous. It is noted that this rocedure can be used most efficiently in solving problems that are characterized by a complicated shape of he region of calculation. Results of solving two problems obtained by means of software pakages that use the uggested procedure are presented.

Numerical solution of three-dimensional problem of high-speed interaction of a cylinder with a rigid barrier, taking into account thermal effects

Analysis of three-dimensional problems associated with high-speed interaction of deformed solids with a solid barrier over a broad range of angles of impact constitutes a task of the highest priority. However, none of the studies of asymmetric impact, either in the two- or the three-dimensional formulation, that have been conducted up until now have focused on the subject of thermal effects. In addition, from ana analysis of studies that have been devoted to axisymmetric problems of high-speed impact, it is clear that the dependence of the characteristics of the material on temperature must be taken into account in order to arrive at a correct description of the processes of strain and destruction of bodies subjected to asymmetric loading. In the present article numerical simulation fo high-speed interaction of cylindrical strikers with a rigid barrire is conducted over a broad range of angles of impact, taking into account the influence of the temperature patterns that are realized in the cylinders in the course of impact.

Numerical solution of three-dimensional problem of free vibrations of composite laminated anisotropic shells of revolution

1. In free vibrations in laminated anisotropic shells, a complex strain state appears, with a three-dimensional character. 2. If anisotropy is ignored, the calculated value of the natural frequency is considerably overstated; the error increases with increasing number of the waves in the circular direction. 3. Calculation of an anisotropic shell on the basis of the orthotropic model may give incorrect representations of the alternation of the lowest modes of vibration, which cannot be tolerated in formulating elastic dynamic models of the objects of investigation.

On the use of hybrid grid-characteristic schemes for the numerical solution of three-dimensional problems in the dynamics of a deformable solid

The three-dimensional dynamical problem of the oblique impact of a rigid pellet on a deformable elastoplastic barrier is solved using a hybrid grid-characteristic scheme for the numerical solution of non-stationary systems of hyperbolic equations. Thegrid-characteristic hybrid scheme is adapted for the numerical solution of multidimensional non-stationary problems in the mechanics of deformable bodies.

A Numerical Solution of Three-Dimensional Problems in Dynamic Elasticity

The equations governing the dynamic deformation of an elastic solid are considered as a symmetric hyperbolic system of linear first-order partial-differential equations. The characteristic properties of the system are determined and a numerical method for obtaining the solution of mixed initial and boundary-value problems in elastodynamics is presented. The method, based on approximate integral relations along bicharacteristics, is an extension of the method proposed by Clifton for plane problems in dynamic elasticity and provides a system of difference equations, with second-order accuracy, for the explicit determination of the solution. Application of the method to a problem which has a known solution provides numerical evidence of the convergence and stability of the method.