关于修正的功的互等定理的讨论

Discussion on the Modified Reciprocal Theorem of Works

以线弹性直梁系统为例,对Betti-Maxwell功的互等定理与修正的功的互等定理进行了比较研究.研究发现处于真实状态的两个不同的直梁系统均可等效地转化为同一直梁受两组不同外力作用的系统,进而揭示了修正的功的互等定理中"两个不相同的线弹性体"即为位移和力的边界条件相互等效的同一个结构.所以,"修正的功的互等定理"实际上仍是Betti-Maxwell功的互等定理的另一种表现形式.

A comparative study was demonstrated between the Betti-Maxwell reciprocal theo- rem of works and the modified reciprocal theorem of works in view of linear-elastic beam sys- tems. It is indicated that 2 different beam systems under the real equilibrium states can be e- quivalently transformed into an identical beam system subjected to 2 sets of different external forces. Moreover, it is revealed that the ＇ 2 different linear elastic bodies＇ in the modified recip- rocal theorem of works are the same structure with equivalent boundary conditions of displace- ments and forces. Consequently, the modified reciprocal theorem of works is actually an alter- native representation of the Betti-Maxwell reciprocal theorem of works.