一种考虑温度影响的高效几何非线性梁柱单元

An Efficient Geometric Nonlinear BeamColumn Element Considering Temperature

摘要:

在梁柱单元位移函数中引入了轴力的影响，将传统3次位移函数改进为4次位移函数，并推导得到了考虑温度影响的几何非线性梁柱单元.该单元的几何非线性刚度矩阵中完整考虑了单元位形变化对平衡方程的影响、温度变化对材性和单元应变的影响以及单元位形变化对几何方程的影响，进而可以考虑二阶效应、弓形效应.采用该单元编制了有限元程序，算例分析表明，该梁柱单元精度得到了显著改善，可以极大减少非线性有限元模型的单元数量，在分析火灾下梁的悬链线效应、火灾下杆系结构连续性倒塌等问题上具有显著优势.

关键词:梁柱单元; 几何非线性; 单元刚度矩阵; 弓形效应; 温度

Abstract:

Instead of traditional cubic Hermitian interpolation function, axial force is considered in element deformation in this paper, and a fourth order interpolation function is employed to form a new beamcolumn element considering thermal effect. Influence of element deformation on equilibrium equation and geometric equation, and influence of temperature on material properties and strain formulation are considered in new element, known as secondorder effect and bowing effect. A finite element program was written to verify the efficiency and accuracy of the new element against B23 in ABAQUS. It is concluded that the element number can be greatly reduced under the same accurate condition, and be superior in dealing with limit analysis, such as catenary effect of beam in fire and nonlinear progressive collapse analysis in fire.

Key words:beamcolumn element; geometric nonlinearity; element stiffness matrix; bowing effect; temperature