MATHEMATICA在推导梁柱单元刚度矩阵中的应用

The Application Of The MATHEMATICA Software In Deducing Beam Element Stiffness Matrix

利用MATHEMATICA强大的运算能力,将考虑多种因素相互作用下的空间梁复杂的刚度矩阵的推导,化做简单的公式运算,避免了繁琐的编程调试和元素寻址,得到了能够考虑拉压、弯曲、剪切、扭转、翘曲耦合影响下的空间梁单元刚度矩阵。在推导过程中,根据影响因素的不同,运用分块技术,将刚度矩阵分解为若干块的正应力刚度矩阵、剪应力刚度矩阵,以及相互影响的相关矩阵,实现了对刚度矩阵的贡献分析。算例进一步验证了所得结果的正确性和优越性。

This paper makes use of the powerful operation ability of the Mathematica software, simplifies the complicated deducing process of the element stiffness matrix of the space beam of loading manifold factors into the formulation operation, avoids the troublesome program debugging and variable addressing, and gets an element stiffness matrix considering the coupling affects of pulling and pressing, bending, shearing, torsion and warping. The matrix deduced by using the parting technique consists of several parts： the normal stress stiffness matrix, the shearing stress stiffness matrix, and the correlated stiffness matrix. Every part of the stiffness matrix has definite meaning and can be used to analyze the coupling influence of every factor, the result can be more mature and exact, and very convenient to be proceeded for the theoretic analysis,