用等效力系变换矩阵求解静不定桁架极限载荷

采用等效力系变换矩阵研究了双模量静不定桁架极限载荷问题．首先证明了固体的等效力系变换矩阵与等效位移变换矩阵是互为转置的矩阵，采用等效力系变换矩阵求解双模量静不定桁架结构的内力，然后再利用静力方程确定双模量静不定桁架结构的极限载荷．当力的变换关系可以根据物理条件容易求得，而位移的变换关系不容易找出时，用等效力系变换矩阵求解静不定桁架极限载荷，就更能显示出其计算过程简洁、清晰等优点．用等效力系变换矩阵求解静不定桁架极限载荷不涉及材料的性质，对各向同性材料、双模量材料静不定桁架极限载荷的求解都适用．

Calculating Ultimate Load of Statically Indeterminate Truss by the Equivalent Force System Transformation Matrix

In this paper, the equivalent force system transformation matrix is used to study the ultimate load of the bimodal statically indeterminate truss. Firstly, the equivalent force system transformation matrix and the displacement transformation matrix are proved to be transpose of each other for the elastic body. Secondly, the equivalent force system transformation matrix is used to calculate the internal force of the bimodal statically indeterminate truss. Finally, the static equations are utilized to determine the ultimate load of the bimodal statically indeterminate truss. When the force transformation matrix can be easily obtained from the physical condition and the displacement transformation matrix is not easy to find, the method using the equivalent force transformation matrix shows significant advantages of clearness and concision in calculating the ultimate load of statically indeterminate truss. This method is independent of the material properties and is applicable to solve the ultimate load of the bimodal statically indeterminate truss of isotropic material.