Unified Way for Dealing With Three-Dimensional Problems of Solid Elasticity
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摘要: 依据三维弹性力学问题的Kelvin解,用三维虚边界元法来建立积分方程,从而使三维实体和各类板、壳等问题的求解思想得到统一.对各类三维问题采用统一的思想建立数学模型,更有利于程序模块化,增强了程序的通用性.另外,建立积分方程时直接引用Kelvin解,而未引入任何其它假设,使该方法的解更偏于实际,且使应用范围拓宽.再者,与边界元直接法相比,该方法的优点在于无需处理奇异积分,且系数阵是对称的.最后给出部分算例,以证明方法的有效性和计算精度.Abstract: Unified way for dealing with the problemsal of three dimensional solid, each type of plates and shells etc. was presented with the virtual boundary element least squares method(VBEM). It proceeded from the differential equations of three-dimensional theory of elasticity and employs the Kelvin solution and the least squares method. It is advantageous to the establishment of the models of a software for general application to calculate each type of three-dimensional problems of elasticity. Owing to directly employing the Kelvin solution and not citing any hypothesis, the numerical results of the method should be better than any others. The merits of the method are highlighted in comparison with the direct formulation of boundary element method(BEM). It is shown that coefficient matrix is symmetric and the treatment of singular integration is rendered unnecessary in the presented method. The examples prove the efficiency and calculating precision of the method.
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