状态空间法分析矩形厚薄板的弯曲

ANALYSIS OF BENDING OF THICK THIN PLATES BY STATE SPACE APPROACH

基于三维弹性力学控制方程，导出矩形厚薄板的状态方程。应用三角函数来构造矩形板的两类场变量函数，即位移与应力场函数，由状态方程解出板的全部位移与应力分量，其中包括三个位移分量和六个应力分量。通过算例表明，状态空间法能获得厚薄板的统一解答，由于板作为空间问题来求解润而不会遇到象有限元求解厚薄板过渡问题时所产生的“自锁”现象。

Based on control equations of three dimensional elasticity, the state equations of thick thin plate have been derived. The two kinds of field functions (displacements and stresses) are constructed by using the triangle functions, all the displacement and stress components (including u, v,w and σx,σy,σz,τxy,τyz,τzx) are solved from the state equations. An example is given,the unification solution of thick thin can be obtained. Since the plate is considered as space problem, so the 'lock' phenomenon does not happen as in the thick thin plates soultion by using finite element method.