This paper presents a generalized constrained differential quadrature method to investigate the elastoplastic dynamic response and ultimate bearing capacity of beam-plate coupled structures under uniaxial compression, compression-bending and compression–shear loadings, considering the interaction between plates and beams. A beam-plate coupled structure is divided into some plate elements, considering the compatibility between contiguous plate elements using the penalty function method which can solve the problem of beam-plate deformable connection of different materials. Virtual work principle and generalized constrained differential quadrature method are used to derive the dynamic governing equations of the beam-plate in which the geometrical and material nonlinearity is considered in the paper. The iterative Newmark/Newton–Raphson method is used to solve the governing equations of the beam-plate. The verification analysis is carried out to demonstrate the accuracy of the proposed method by comparison with the results from FEM. Then, various effects of the rotational spring stiffness, width-to-thickness ratio, aspect ratio, impact time and coupling load on the elastoplastic dynamic response and ultimate bearing capacity of beam-plates are evaluated.

本文提出了一种广义约束微分正交方法，研究了考虑板与梁相互作用的单轴压缩，压弯和压剪荷载作用下梁-板耦合结构的弹塑性动力响应和极限承载力。考虑到连续板单元之间的相容性，采用罚函数法将梁板耦合结构分为若干板单元，可以解决不同材料的梁板变形连接问题。利用虚拟工作原理和广义约束差分正交方法，导出了考虑几何和材料非线性的梁板动力学控制方程。迭代的Newmark / Newton-Raphson方法用于求解梁板的控制方程。通过与有限元分析结果进行比较，进行了验证分析，以证明所提方法的准确性。然后，评估了旋转弹簧刚度，宽厚比，长宽比，冲击时间和耦合载荷对梁板弹塑性动力响应和极限承载力的各种影响。