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Taylor meshless method for thin plates

Abstract : A new class of meshless method – Taylor Meshless Method (TMM) - has been introduced that relies on an explicit solution of the Partial Differential Equations inside the domain with the help of Taylor series expansions. Because the PDE is solved analytically in the domain, one is reduced to a discrete boundary problem whose size is rather small.The effectiveness and efficiency of TMM have been verified by solving some partial differential equations. In the cases that have been studied, TMM is robust and effective. For 2D linear problems, one domain is sufficient to solve boundary value problems.TMM is used to solve Kirchhoff plate problems. Techniques in TMM help to reduce the degree of freedoms significantly so that one can increase the degree of the polynomials to a very high level. Laminated sandwich plates are studied by using TMM. Different cases are considered to test the effectiveness and efficiency of the method. The error shows exponential convergence with the increase of degree of polynomials.TMM is combined with asymptotic-numerical method (ANM) to solve large deflection problems of thin plates. The nonlinear equations are expanded in the form of power series, which leads the problem to a series of linear equations. The step length is determined automatically by a reliable path following technique. The accuracy and efficiency of ANM-TMM is verified through these examples and the method can be easily extended to other nonlinear problems.Based on the work of bending problems, the buckling of thin plates are studied. This approach fully takes the advantage of the path following technique. Thus the buckling process can be illustrated much more accurate than that by other methods. The performance of the approach is investigated by a series of benchmark buckling problems.The membrane wrinkling problems are studied. Different tension loads and imperfections are imposed to test their influence on final wrinkle patterns. The results show that TMM can accomplish convergent simulations with very small imperfections and tension loads in comparison with finite element methods. The approach of wrinkled membrane analysis by TMM has been well established.
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Submitted on : Tuesday, February 18, 2020 - 11:29:10 AM
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  • HAL Id : tel-02482710, version 1

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Haitao Tian. Taylor meshless method for thin plates. Other [cond-mat.other]. Ecole nationale supérieure d'arts et métiers - ENSAM, 2019. English. ⟨NNT : 2019ENAM0036⟩. ⟨tel-02482710⟩

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