空间梁单元显式切线刚度矩阵推导

Derivation of Explicit Tangent Stiffness Matrix for Space Beam Element

在开展桥梁、房屋、网壳、网架等杆系结构几何非线性分析或极限承载力计算时,需要空间梁单元的切线刚度矩阵。基于非线性问题的一般平衡方程和空间梁单元的非线性几何方程,推导应力应变一般线弹性关系下的空间梁单元显式切线刚度矩阵,该刚度矩阵中包含了由初应力和初应变产生的初应力刚度矩阵,为空间有限元程序的编制奠定了基础。

When carrying out geometric nonlinear analysis or ultimate bearing capacity calculation for stem structures such as beam, roof, reticulated shell structures or grid structures, tangent stiffness matrix of space beam element is requested. The explicit tangent stiffness matrix of space beam element under general linear elastic relationship of stress and strain shall be derived based upon general balance equation of nonlinear questions or nonlinear geometric equation of space beam element, this stiffness matrix contains initial stress stiffness matrix generated from initial stress and initial strain, which establishes the foundation for compiling space finite element programs.