含无限刚性体的杆系内力的一种新的计算方法

A New Method for Internal Forces Calculation in Bar Elements with Infinite Stiffness

含无限刚性体的杆系内力计算,传统解法是将拉压或弯曲无限刚度近似用有限大值来代替,通过数值计算确定杆系内力。计算表明,当刚度取值足够大值时,经常会造成方程组的病态而严重影响求解精度。本文提出一种精确解法,即通过引入无限刚度杆刚性约束方程来避免病态方程等问题,从而保证了计算的有效性和精确度。本文具体对具有拉压和弯曲无限刚度杆系单元建立了相应的约束方程,并针对工程中典型的支座形式:铰支座、滚轴支座和斜向支座给出了约束条件。作为一个具体应用,本文对于一平面刚架结构,利用建立的约束方程并通过确定结点定位向量和单元定位向量,最终获得了结构内力。算例结果表明,本文方法适用于分析含无限刚性体的杆系内力。

Traditionally the internal forces in bar elements with infinite tensional/compressive or bending stiffness are determined approximately based on the large finite values of two parameters. Such a treatment usually leads to the governing equations become ill-posed equations and thus may influence the accuracy in calculation. A new analytical method was proposed by constructing corresponding equations of constrains, which can avoid the possible resulting ill-posed equations and guarantee the effectiveness and exactness in computation. Meanwhile, the corresponding equations of constrains were also given for several classical forms of boundary support： tumbler, rolling, and angle bearing restraints. As an application, the resulting equations of constrains were used to determine both joint and element location vectors for a plane framed structure, and the internal forces were derived finally. The computational results show the present method is valid for the internal forces calculation in such bar elements.