基于空间受力性能最优化的箱梁带斜梁空间刚架模型

Spatial Grid Model with Diagonal Beam Elements Based on the Optimization of Spatial Mechanical Behaviors

提出一种新型的带斜梁空间刚架模型,可用于混凝土箱梁结构在线弹性阶段的空间受力分析。以带斜梁空间刚架模型和真实平板在面内轴压、面内纯剪、面外纯弯这三种基本荷载作用下变形的相对误差绝对值作为目标函数,以该模型中纵横梁和斜梁的截面特性作为可变参数,以目标函数达到最小值作为优化目标,通过求解该最优化问题,建立空间性能最优化的带斜梁空间刚架模型。采用集中荷载下的悬臂梁和均布荷载下的简支箱梁作为示例,对提出的模型进行了验证,结果表明:带斜梁空间刚架模型不受平截面假定的限制,可较准确地模拟空间结构的弯曲刚度和面内剪切刚度,其变形计算结果和计入剪切变形的材料力学理论解、实体模型结果基本吻合。

A novel spatial grid model with diagonal beam elements is proposed to analyze the spatial mechanical behaviors of concrete box-section girders at the elastic linear state.The establishment of the model is based on an optimization problem:the objective functions are the absolute relative differences between the deformations from the proposed model and the actual plate under three basic types of loads including in-plane axial compression,in-plane shear,and out-of-plane bending;the variable parameters of the functions are the properties of vertical and horizontal beam and diagonal beam elements in the proposed model;the objective for the optimization is to minimize the objective functions.By solving the optimization problem,the spatial grid model with diagonal beam elements based on the optimization of spatial mechanical behaviors is established.The validity of the proposed model is illustrated with a cantilever beam under a concentrated load and a simply supported box-section girder with uniform loads as case examples.The results show that the spatial grid model with diagonal beam elements is not limited by the plane section hypothesis and is capable of accurately predicting the bending stiffness and in-plane shear stiffness.The results also reveal that the proposed model can yield deformation results consistent with the solution based on the mechanics of materials considering shear deformations and with the results from solid element models.