Ningjie Wang¹, Yihao Wang¹, Yongle Pei², Luxian Li^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.1, pp. 171-186, 2024, DOI:10.32604/cmes.2024.053520 - 20 August 2024

Abstract A numerical approach is an effective means of solving boundary value problems (BVPs). This study focuses on physical problems with general partial differential equations (PDEs). It investigates the solution approach through the standard forms of the PDE module in COMSOL. Two typical mechanics problems are exemplified: The deflection of a thin plate, which can be addressed with the dedicated finite element module, and the stress of a pure bending beam that cannot be tackled. The procedure for the two problems regarding the three standard forms required by the PDE module is detailed. The results were 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 More >