基于平面梁单元的分阶段成形结构线形控制方程

摘要

To probe into the relationship between the final target geometric shape and the unstressed state amounts of the structure formed in stages,the geodetic coordinates are chosen as the reference for the target geometric shape,the external force potential is defined as the force potential relative to the coordinate axes and by taking the unstressed state of the elements as the starting point,the total strain energy of the structure is calculated.On the principle of the stationary potential energy,the equation for the geometric shape control of the structure is established.The equation can determine exclusively the unstressed state amounts of the various elements in the structure according to the target geometric shape.As long as the elements can be installed according to the element configuration corresponding to the unstressed state amounts,the geometric shape of the formed structure will be bound to automatically approximate the target geometric shape and will be irrelevant to the specific formation process of the structure.The analysis of a numerical example shows that the equation for the geometric shape control as established in this paper is accurate and reliable and can be applied to the calculation of the geometric shape control of the structure formed in stages.%为探讨分阶段成形结构最终目标线形与无应力状态量的关系,选择目标线形以大地坐标为参照,将外力势定义为外力相对于坐标轴的力势,以单元无应力状态作为起点计算结构总应变能.由势能驻值原理建立结构线形控制方程,该方程根据目标线形可以惟一确定结构中各个单元的无应力状态量,只要保证各个单元按照无应力状态量对应的单元构形进行安装,成形后的线形必将自动逼近目标线形,与具体的成形过程无关.通过数值分析表明,所建立的线形控制方程是准确可靠的,可用于分阶段成形结构的线形控制计算.