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  • Open Access

    ARTICLE

    PDE Standardization Analysis and Solution of Typical Mechanics Problems

    Ningjie Wang1, Yihao Wang1, Yongle Pei2, Luxian Li1,*

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

    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 >

  • Open Access

    ARTICLE

    Exact Large Deflection Solutions for Timoshenko Beams with Nonlinear Boundary Conditions

    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 >

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