Abstract

This paper reports new h-, hp-, and p-versions of the least squares collocation (LSC) method of high-order accuracy proposed and implemented for solving boundary value problems for biharmonic-type equations in regular and irregular domains. The solutions of these equations are used to model and analyse the stress-strain state of isotropic and orthotropic thin plates. In particular, irregular plates with circular holes are considered here. It is shown that our approximate solution is high order accurate. We represent some suitable numerical examples. In addition, the plate on elastic foundation is considered.

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