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On the use of Radial Point Interpolation Method (RPIM) in a high order continuation for the resolution of the geometrically nonlinear elasticity problems

机译：在高阶连续中使用径向点插值法（RPIM）来解决几何非线性弹性问题

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摘要

In this work, we propose a new high order algorithm based on the coupling of Radial Point Interpolation Method (RPIM) and a high order continuation to solve the geometrically nonlinear elasticity problems under a strong formulation. The high order continuation has an adaptive step length which is very efficient and performed especially for solving the nonlinear problems. The specificity of RPIM is the exact implementation of boundary conditions because its shape functions have the Kronecker delta function property as in the conventional Finite Element Method (FEM). Therefore, it has proven that the RPIM shape functions have not only possess all advantages of the enforcing boundary conditions, but also can accurately reflect the properties of stresses distribution. This algorithm allows obtaining the solution with a less expensive CPU time to that of incremental iterative methods. A numerical comparison between the proposed algorithm and the others of literature is illustrated on some examples of geometrically nonlinear elasticity problems.
机译：在这项工作中，我们提出了一种新的基于径向点插值方法（RPIM）和高阶连续性的耦合的高阶算法，以解决强约束下的几何非线性弹性问题。高阶连续具有自适应步长，该步长非常有效，尤其是在解决非线性问题时执行。 RPIM的特殊性是边界条件的精确实现，因为它的形状函数具有传统有限元方法（FEM）中的Kroneckerδ函数性质。因此，已经证明，RPIM形状函数不仅具有强制边界条件的所有优点，而且可以准确地反映应力分布的特性。与增量迭代方法相比，该算法可以用较少的CPU时间获得解决方案。在几何非线性弹性问题的一些示例中，说明了所提算法与其他文献的数值比较。

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