离散平面结构的相容条件
Compatibility Conditions for Discrete Planar Structure
摘要：
研究了由节点和连接杆组成的平面网络结构的协调条件，这些条件限制杆的伸长量，类似于连续介质力学中变形的协调条件。变形保持平面的要求强加了兼容性。考虑了给定长度结构的相容性及其线性化问题。对于三角形结构，相容性表示为围绕每个内部节点的星域的边长的多项式方程。这些条件的连续极限与连续问题的连续极限一致。相容性方程可以沿一条闭合曲线求和，给出类似于Gauss-Bonnet积分公式的条件。与连续材料相比，刚性桁架没有协调条件。洞周围的协调方程涉及洞周围邻域中的边。协调条件的数量是在保持结构刚性的同时可以从结构中移除的杆的数量;该数量测量结构弹性。分析了相容性条件的渐近密度。
英文摘要：
Compatibility conditions are investigated for planar network structures consisting of nodes and connecting bars; these conditions restrict the elongations of bars and are analogous to the compatibility conditions of deformation in continuum mechanics. The requirement that the deformations remain planar imposes compatibility. Compatibility for structures with prescribed lengths and its linearization is considered. For triangulated structures, compatibility is expressed as a polynomial equation in the lengths of edges of the star domain surrounding each interior node. The continuum limits of the conditions coincide with those in the continuum problems. The compatibility equations may be summed along a closed curve to give conditions analogous to Gauss-Bonnet integral formula. There are rigid trusses without compatibility conditions in contrast to continuous materials. The compatibility equations around a hole involve the edges in the neighborhood surrounding the hole. The number of compatibility conditions is the number of bars that may be removed from a structure while keeping it rigid; this number measures the structural resilience. An asymptotic density of compatibility conditions is analyzed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
