基于弱形式求积元的Timoshenko梁弹塑性分析

Elastoplastic Analysis of Timoshenko Beam Based on Weak-form Quadrature Element Method

应用塑性形变理论,建立了基于弱形式求积元的Timoshenko梁弹塑性分析方程,利用全量初应力矩阵迭代法对方程进行求解.进一步编制了程序对两端固支、横截面分层钢梁进行了弹塑性分析,并与商用有限元软件MIDAS结果进行比较,验证了该方法的正确性.研究表明,将弱形式求积元法应用于弹塑性分析,与有限元方法相比,无需细分单元就能得到较为精确的结果;与微分求积法相比,处理材料非线性问题更为灵活、方便.

The elastic-plastic equations of Timoshenko beam based on weak-form quadrature element method is established by deformation theory and solved by employimg the whole amount method of initial stress.The plastic analysis program of the clamped,layered steel beam corss-section is given.Compared with the commercial finite element software MIDAS,the results verified the validity of the method and showed that compared with the finite element method,for the weak form quadrature element method was applied to elastic-plastic analysis,more accurate results could be obtained without sub-unit;and compared with the differential quadrature method,it can deal with material nonlinearity more flexibly and conveniently.