非线性材料杆系结构的内力求解

随着科技的发展，已研发出了许多非线性材料，这些非线性材料组成的结构已在工程实际中得到了广泛应用．本文研究了静不定非线性材料结构杆件内力的求解这一关键问题．利用非线性材料结构余能及静力平衡条件，构造了新泛函数，对新泛函数进行一阶求导，即可方便求得静不定非线性材料结构杆件的内力．同时，指出了非线性材料杆系结构的内力求解时存在漏解的原因：结构材料的应力与应变本构关系为非线性幂函数，把结构余能对杆系的内力求一阶偏导，令所得到的位移方程等于零，该方程为一元二次方程，应有两个实数解，而有关文献却遗漏了一个实数解．

Internal Force Solution for the Bar Structure Made of Nonlinear Materials

With the development of science and technology, many nonlinear materials have been developed. Structures composed of these nonlinear materials have been widely used in engineering practice. Therefore, it is the important to solve the internal force of the statically indeterminate structure made of nonlinear materials. Based on the complementary energy and the static equilibrium condition of the nonlinear material structure, a new general function is constructed. The first derivative of the new universal function can be used to calculate the internal forces of statically indeterminate nonlinear material structures. At the same time, it is pointed out that the reason of missing solution in solving the internal force of the nonlinear material bar system is that the stress-strain constitutive relation of the structural material is a nonlinear power function. Solving the quadratic displacement equation that the first derivative of the complementary energy regarding to the stress equals to zero, there should exist two real solutions. However, a real solution was omitted in the previous literature.