基于平面梁单元的几何非线性分阶段成形平衡方程

发布时间：2018-07-17 01:56

【摘要】：为探讨几何非线性条件下基于平面梁单元分阶段成形结构最终状态的影响因素,结合其成形特点,以结构的无应力状态为分析起点计算结构系统的总势能,根据最小势能原理,建立结构分阶段成形时不考虑其成形过程的力学平衡方程,获得结构最终状态与平面梁单元无应力状态量的关系,在全量列式平衡方程的基础上,推导出增量列式求解方程,并通过算例说明平衡方程的应用。对计算结果和平衡方程的分析表明:对于由梁单元组成的分阶段成形结构,当结构体系、外荷载和边界条件一定时,即使在考虑结构几何非线性效应的前提下,其最终状态的确定只与梁单元的无应力长度和无应力曲率有关,与其成形过程无关。
[Abstract]:In order to discuss the influence factors of the final state of the structure based on the plane beam element stage forming under the geometric nonlinear condition, combining with its forming characteristics, the total potential energy of the structure system is calculated with the non-stress state of the structure as the starting point, according to the principle of minimum potential energy. In this paper, the mechanical equilibrium equation of the structure is established without considering the forming process, and the relationship between the final state of the structure and the unstressed state of the plane beam element is obtained. On the basis of the equilibrium equation of the total formula, the incremental equation for solving the equation is derived. An example is given to illustrate the application of the equilibrium equation. The analysis of the calculation results and the equilibrium equation shows that when the structural system, external load and boundary conditions are fixed, even when the geometric nonlinear effect of the structure is considered, for the phased forming structure composed of the beam element, the structural system, the external load and the boundary conditions are fixed, even if the geometric nonlinearity of the structure is taken into account. The determination of the final state is related only to the length and curvature of the beam element, but not to the forming process.
【作者单位】：西南交通大学土木工程学院;中铁大桥勘测设计院集团有限公司;中铁大桥局集团有限公司;
【基金】：国家科技支撑计划(2012BAG05B02) 国家重点基础研究发展计划(973计划)(2012CB026205)~~
【分类号】：U441

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