US-FE-LSPIM四边形单元的静力和强迫振动分析

US-FE-LSPIM QUAD4 Element for Static and Forced Vibration Analysis

US-FE-LSPIM四边形单元由使用不同的形函数作试函数和检验函数而构成。传统的四节点等参形函数作检验函数,用于满足单元内和单元间的位移连续条件。FE-LSPIM四边形单元的形函数作试函数,用于满足所有的位移完备性条件。与FE-LSPIM四边形单元相比,该单元不需要通过使用罚函数法或拉格朗日乘子法使得整段边界满足位移边界条件。应用其分析静力和强迫振动问题。典型算例表明,对于静力和强迫振动问题,该单元在稀疏和畸变的网格时具有较高的精度,优于四边形Q4单元和QM6单元。

The US-FE-LSPIM QUALM element is developed by using two different sets of shape functions for the trial and test functions. Classical isoparametric shape functions, as test functions, are used to satisfy require- ment of displacement the intra- and inter-element continuity. And shape functions of FE-LSPIM QUAD4 element, as trial functions, are used to satisfy all the displacement completeness requirements. And by compared with FE- LSPIM QUALM element, the proposed element does not need to use penalty method or lagrange multiplier method to ensure fulfilment of exact essential boundary condition along the entire length of the edge. This element is extended to static and forced vibration analysis. Typical test examples show that for static and forced vibration problem the US-FE-LSPIM QUAD4 element has good accuracy under coarse and distorted meshed and is superior to quadrilater- al Q4 element and QM6 element.