Extended rod theory including two-dimensional stiffness of structures

结构是由许多不同结构刚度的结构部件组成的。以往的一维杆理论对于简化解析法来说是有效的，但由于局部刚度的变化，它不能考虑结构的行为。对于高层建筑等复杂结构，以及具有不规则层的结构与地基的相互作用，需要进行包括二维结构变化在内的简化分析。研究的目的是提供一种简化分析二维变刚度结构动力行为的一般理论。(1)考虑结构二维刚度影响的延伸杆理论从哈密顿原理出发，建立了考虑轴向变形、弯曲变形、横向剪切变形和局部变形影响的延伸杆理论。通过与其他分析方法的比较，证明了该理论的正确性。阐述了不规则层结构与土的相互作用效应，研究了二维刚度对结构与不规则层土相互作用的影响，阐明了结构与不规则层土的相互作用效应，给出了结构与不规则层土相互作用的简化理论。对于包括不规则固体层效应在内的新问题，研究了抛掷巨石对地震振动的影响的基本数据和建议的理论。

Structures are composed of many structural parts which are different structural stiffness. The previous one-dimensional rod theory which grasps the global structural behavior is effective as for simplified analytical method, but it cannot consider the structural behavior due to local variation of stiffness. The simplified analysis including the two-dimensional structural variation is necessary to complicate structure such as high-rise building with setback, and the interaction between structure and ground with irregular layer. The aim of research is to present a general theory to simply analyze the dynamic behavior of structure with two-dimensional variation of stiffness. And the following dynamic phenomena are clarified by means of the theory proposed here.(1) Formulation of extended rod theory including the effect of two-dimensional stiffness of structures The theory including the effect of axial deformation, bending, transverse shear deformation, and local deformation is formulated from the Hamilton principle. The exactness of the proposed theory is proven by comparing with the another analytical methods. The theory is submitted to International journal, in which static, free vibration, force vibration of coupled shear wall with opening are discussed.(2) Clarification of interaction effect between structure and soil with irregular layer The theory included the effect of the two-dimensional stiffness is studied to clarify interaction effect between structure and soil with irregular layer A simplified theory for interaction effect between structure and soil with irregular layer is given from numerical results. The fundamental data and the proposed theory which explain the implication of thrown-out boulders for earthquake shaking is studied for new problem including the effect of irregular layer of solid.