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Meshfree stabilized collocation method in elasticity[J].计算力学学报,2021,38(3):305~312

Meshfree stabilized collocation method in elasticity
Meshfree stabilized collocation method in elasticity

DOI：10.7511/jslx20210115001

 作者 单位 E-mail 王莉华 同济大学 航空航天与力学学院, 上海 200092 lhwang@tongji.edu.cn 刘义嘉 同济大学 航空航天与力学学院, 上海 200092 钟伟 同济大学 航空航天与力学学院, 上海 200092 钱志浩 同济大学 航空航天与力学学院, 上海 200092

伽辽金型无网格法具有精度高、稳定性好的优点，但是实现高阶准确积分过程复杂，计算效率低。配点型无网格法的计算效率高，但是其在求解复杂问题时往往会出现精度和稳定性较差的结果。本文介绍一种新的无网格法-无网格稳定配点法，采用重构核近似作为近似函数，在规则子域内非常容易实现高阶准确积分，既保留了配点型无网格法效率高的特点，又具备伽辽金型无网格法精度高和稳定性好的特点，而且还兼具有限体积法满足局域离散方程守恒的特点。通过弹性力学算例验证了该算法的优越性，未来可将其进一步应用于流体和流固耦合问题分析。

Galerkin-type meshfree methods have the advantages of high accuracy and good stability,but the process of achieving high-order accurate integration is complicated,which results in the low efficiency of such methods.The collocation-type meshfree methods have high computational efficiency,but they often suffer from poor accuracy and stability when solving complex problems.Therefore,this paper introduces a new meshfree method-meshfree stabilized collocation method.In this method,the reproducing kernel function is utilized as the approximation function.Regular subdomains are established to achieve the high-order accurate integration.This method not only possesses the high efficiency as the direct collocation method,but also has the high accuracy and good stability as the Galerkin-type meshfree methods.Besides,it is also characterized by satisfying the conservation of local discrete equations as the finite volume method.Several examples of elasticity problems are presented to verify the superiority of the proposed method.It can be further applied to fluid and fluid-structure interaction problems in the future.