Zhuowan Fan¹, Yancheng Liu¹, Anyu Hong^1,*, Fugang Xu^1,*, Fuzhang Wang²

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.1, pp. 341-355, 2022, DOI:10.32604/cmes.2022.019715

Abstract In this work, the localized method of fundamental solution (LMFS) is extended to Signorini problem. Unlike the traditional fundamental solution (MFS), the LMFS approximates the field quantity at each node by using the field quantities at the adjacent nodes. The idea of the LMFS is similar to the localized domain type method. The fictitious boundary nodes are proposed to impose the boundary condition and governing equations at each node to formulate a sparse matrix. The inequality boundary condition of Signorini problem is solved indirectly by introducing nonlinear complementarity problem function (NCP-function). Numerical examples are carried out to validate the reliability… More >

Sen Yung Lee¹, Shin Yi Lu², Yen Tse Liu², Hui Chen Huang²

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 293-312, 2008, DOI:10.3970/cmes.2008.033.293

Abstract A new analytic solution method is developed to find the exact static deflection of a Timoshenko beam with nonlinear elastic boundary conditions for the first time. The associated mathematic system is shifted and decomposed into six linear differential equations and at most four algebra equations. After finding the roots of the algebra equations, the exact solution of the nonlinear beam system can be reconstructed. It is shown that the proposed method is valid for the problem with strong nonlinearity. Examples, limiting studies and numerical analysis are given to illustrate the analysis. The exact solutions are compared with the perturbation solutions.… More >

Sen Yung Lee¹, Sheei Muh Lin², Chien Shien Lee³, Shin Yi Lu³, Yen Tse Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.1, pp. 27-36, 2008, DOI:10.3970/cmes.2008.030.027

Abstract An analytic solution method, namely the shifting function method, is developed to find the exact large static deflection of a beam with nonlinear elastic springs supports at ends for the first time. The associated mathematic system is a fourth order ordinary differential equation with nonlinear boundary conditions. It is shifted and decomposed into five linear differential equations and at most four algebra equations. After finding the roots of the algebra equations, the exact solution of the nonlinear beam system can be reconstructed. It is shown that the proposed method is valid for the problem with strong nonlinearity. Finally, examples and… More >