基于非线性梁理论的有限质点法

Finite particle method based on nonlinear beam theory

有限质点法是以向量式力学为基础,用有限数量的质点来模拟结构的变形行为,质点的运动由牛顿运动定律来计算。在有限质点法中,质点通过构件相连,构件约束着质点的运动,并且其内力由质点的运动变量来描述。基于向量式力学的基本思想和非线性梁理论,提出了一种新的有限质点法,该方法在共旋单元坐标系中描述梁的非线性变形。以空间梁系结构为例,推导了计算构件内力的非线性公式,并考虑了弯扭耦合变形。通过两个连续欧拉角的变换公式得到共旋坐标系的旋转矩阵。与传统的有限质点法相比,本文提出的方法避免了刚体虚转动分析。通过四个结构的数值求解,验证了本文方法在计算结构大变形响应时具有较高的精度。

The finite particle method (FPM) is based on vector mechanics.In this method,a finite number of particles calculated by Newton's law of motion are used to simulate the deformation behavior of structures.In FPM,the particles are connected by the components,which restrict the motion of the particles,and the internal force of the component is described by the motion variables of the particles.Based on the basic idea of vector mechanics and nonlinear beam theory,a novel FPM is proposed in this paper.In this method,the nonlinear deformation of the beam is described in the co-rotational element coordinate system.Taking the spatial beam structures as an example,the nonlinear formulas of calculating the internal force of the component are derived,and the bending and twist coupling deformation is considered.The rotation matrix of co-rotational element coordinate system is obtained by the transformation formula of two successive Euler angles.Compared with the traditional FPM,the proposed method avoids the analysis of rigid body virtual rotation.Numerical solutions are presented for four structures,which indicate that the presented FPM algorithm is highly accurate in predicting large deformation responses of structures.