一种新的集成非线性杆件单元刚度矩阵的方法
A NEW METHOD FOR INTEGRATING STIFFNESS MATRIX OF NONLINEAR FRAME ELEMENT
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摘要: 对于非线性杆件单元,本文提出一种新的简便有效的集成单元刚度矩阵的算法。该方法直接从结构力学中的位移法的概念出发,通过解析积分或数值积分求解积分算子,由积分算子线性组合,能快速求解考虑弯、剪、扭、轴压等各种非线形刚度的杆件单元的刚度矩阵。该方法具有广泛的普适性,能适用于所有多项式、插值多项式、解析式、离散点描述的变刚度、变截面直杆的单元刚度矩阵集成计算。文中通过求解线性直杆单元刚度矩阵验证了该方法的正确性。Abstract: A simple and efficient method for integrating the nonlinear beam element stiffness matrix is presented in this paper. It originates from the concept of displacement method of structural mechanics. With either exact or numerical integration and linear combination of integral operators, the element stiffness matrices of nonlinearframe element taking into consideration of bending moment, shear force torsion moment as well as axial force can be obtained easily. The method is universal and valid for various polynomial functions and straight members with varying cross-section or stiffness. An example of straight linear elastic frame is provided to verify the method.