Analyses of cantilever beam problem and nonlinear problem by using sub-domain meshless method - Yong-Ming GUO (The Japan Society of Mechanical Engineers, 2017)
As is well known, a sub-domain method is often used in computational mechanics. The conforming sub-domains, where the sub-domains are not separated nor overlapped each other, are often used, while the nonconforming sub-domains could be employed if needed. In the latter cases, the integrations of the sub-domains may be performed easily by choosing a simple configuration. Then, the meshless method with nonconforming sub-domains is considered one of the reasonable choices for the large-scale computational mechanics without the troublesome integration. We have proposed the sub-domain meshless method (SDMM). It is noted that, since the method can employ both the conforming and the nonconforming sub-domains, the integration for the weak form is necessarily accurate and easy by selecting the nonconforming sub-domains with simple configuration. In this paper, in order to solve more difficult issues, the linear elastic cantilever beam problem and the nonlinear problem are analyzed by using the proposed SDMM. The numerical solutions are compared with the exact solutions and the solutions of the collocation method, showing that the relative errors by using the SDMM are smaller than those by using the collocation method and that the proposed method possesses a good convergence.