基于微分求积法的钢筋混凝土梁静力分析

采用广义微分求积法(GDQM)对钢筋混凝土(RC)梁进行了准静力分析，得到了其抗静载的强度特性．首先，基于虚功原理导出了考虑钢筋和混凝土材料的非线性的RC梁准静力分析控制微分方程，并根据广义微分求积法对其离散，从而得到有限自由度的非线性代数方程组，进而采用Newton-Raphson迭代求解格式，建立了荷载增量法数值分析模型．其次，通过本文GDQM与有限元法分析结果比较，表明了新建算法的正确性；与有限元法的收敛性对比表明本文算法较有限元法有优越性．

Static Analysis of Reinforced Concrete Beam Using the Differential Quadrature Method

Static load bearing capacity of the reinforced concrete (RC) beam was obtained by virtue of the quasi-static analysis of the RC beam, using the generalized differential quadrature method (GDQM). First, the differential equation governing the quasi-static analysis of the RC beam was formulated by the principle of virtual work, where the nonlinear properties of the rebar and concrete were considered. Then, the nonlinear algebraic equations governing the problem with finite degrees of freedom were obtained using the GDQM, and the numerical model was also developed based on the proposed load-incremental Newton-Raphson iteration scheme. Subsequently, the correctness of the proposed method was demonstrated through the comparison between results generated by the present GDQM and finite element method (FEM); the superiority of the GDQM over the FEM on the convergence performance was also studied in the comparison.