Abstract
The paper is devoted to the application of the least-squares collocation method for solving the two- and one-dimensional problems in the mechanics of deformable solids. Calculation results of the deflections of isotropic and orthotropic elastic plates within the framework of various theories are presented. This paper shows that approximate solutions obtained by the hp-version of the least-squares collocation method converge with a high order and agree with analytical solutions of test problems with a high degree of accuracy. Numerical and mathematical modeling of three-point bending of composite beams was carried out taking into account nonlinear stress-strain relationships, multi-modulus behavior, and incipient fracture. It was found that the simulation results are in good agreement with the results of mechanical tests of three-point bending of composite beams.
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