【作者】 杨加明；

【导师】 孙良新；

【作者基本信息】 南京航空航天大学 ， 飞行器设计， 2005， 博士

【摘要】 本文注重对以下三个方面进行研究:即 Kirchhoff 假设条件下复杂边界条件正交各向异性板的几何非线性问题;高阶剪切变形理论下复合材料层合板在复杂边界条件下的几何非线性问题;湿热环境和弹性地基作用下复合材料层合板在弹性转动约束边界条件下的几何非线性问题。 在 Kirchhoff 假设的基础上,对两邻边铰支两邻边夹紧;三边铰支一边夹紧;一边铰支三边夹紧和四边夹紧四种边界条件下正交各向异性矩形薄板进行了几何非线性分析;之后并建立了对 5 种不同边界条件的几何非线性问题统一求解分析方法。对于上述几种不同边界条件的非线性控制方程,选用的位移函数是既能精确满足边界条件又具备正交属性和收敛速度快的梁振型函数。对于不同的边界条件,只需改变梁函数的系数即可,其它架构可保持不变。用“稳定化双共轭梯度法”求解线性稀疏方程组;“可调节参数的修正迭代法”求解非线性代数方程组。本文线性解作为非线性问题的初值迭代,这样能同时得到线性解和非线性解并可对两者进行比较。 利用纵坐标向上的格林公式,证明了当纵坐标向下时的格林公式的有效性,并给出了其三种变化形式,由此导出了二维的分部积分法。利用虚位移原理和二维分部积分法,导出了以 5 个广义位移所表达的高阶剪切变形理论复合材料层合板的几何非线性控制方程和相应的边界条件。利用高阶剪切变形理论,对复杂边界条件的复合材料层合板进行了几何非线性分析。这些边界条件包括:一边铰支三边夹紧、两邻边铰支两邻边夹紧、三边铰支一边夹紧和两对边具有相同弹性系数的弹性转动约束边界条件。之后建立了对总共 6 种边界条件的几何非线性问题统一的求解分析方法。并对 Kirchhoff 假设的板理论所提出的用“稳定化双共轭梯度法”求解线性稀疏方程组和“可调节参数的修正迭代法”求解非线性代数方程组进行了拓展。对于上述几种不同边界条件的几何非线性问题,分析了包括横向剪切变形在内的多个因素对于复合材料中厚板 弯曲性能的影响。 通过对正交各向异性单层正轴和偏轴由湿热膨胀系数产生的应变和双参数地基对板的作用力,推导出一般层合板在高阶剪切变形理论下湿热环境和弹性地基联合作用下的控制方程、边界条件和相应的力学分量公式。探讨了温度、湿度、弹性转动系数、弹性地基参数和铺层数等对层合板非线性弯曲挠度和弯矩的影响。更多还原

【Abstract】 Three aspects of investigations are paid attention to. Those are geometrically nonlinear problems of orthotropic plates under complicated boundary conditions based on Kirchhoff supposition, geometrically nonlinear problems of composite laminated plates under complicated boundary conditions based on higher-order shear deformation theory, geometrically nonlinear problems of composite laminated plates under hygrothermal environments and elastically restrained boundary conditions based on elastic groundsill. Based on the Kirchhoff supposition, geometrically nonlinear bending of orthotropic rectangular thin plates is analyzed under four kinds of boundary conditions of two adjacent edges simply supported and other two adjacent edges clamped, three edges simply supported and one edge clamped, one edge simply supported and three edges clamped, and all four edges clamped. A General solution for nonlinear bending of these plates is established for the five kinds of different boundary conditions. For the nonlinear governing equations of the above different boundary conditions, the selected displacement functions are beam vibration functions that have rapid convergence speed. They accurately satisfy the boundary conditions and possess orthogonal property. The basic framework keeps the same for different boundary conditions, but different coefficients of the beam vibration functions are needed to change. Large scale of linear sparse equations have been solved by Biconjugate Gradients Stabilized Method and nonlinear algebraic equations solved by Parameter-regulated Iterative Procedures. The value of linear solutions is treated as initial value of the nonlinear solutions for iteration. In the way we can find both the linear solutions and the nonlinear ones and compare them. Making use of Green formula when an ordinate is upward, we have proved the validity of Green formula when ordinate is downward. Three other formulae are derived from them. As a result the planar integration by parts is produced. We use the principle of virtual displacements and the planar integration by parts to derive the geometrically nonlinear equilibrium equations and their boundary conditions of composite laminated plates depended on higher-order shear deformation theory in the form of five generalized displacements. By the higher-order shear deformation theory, geometrically nonlinear bending of composite laminated plates is analyzed for complicated boundary conditions. These boundary conditions include one edge simply supported and three edges clamped, two adjacent edges simply supported and other two adjacent edges clamped, three edges simply supported and one edge clamped, and elastic restraint against rotation that has same elastic coefficients for opposite sides. A General solution for geometrically nonlinear bending of these plates is then set up for the six kinds of different boundary conditions. Large scale of linear sparse equations solved by Biconjugate Gradients Stabilized Method and nonlinear algebraic equations solved by Parameter-regulated Iterative Procedures previously for the Kirchhoff plate theory are now extended for the higher-order shear deformation theory. For the geometrically nonlinear problems under above different boundary conditions, effects of several factors including transverse shear deformation are investigated on bending property of moderate composite plates. Using normal or partial strains of a orthotropic lamina due to moisture and temperature and force of double-parameter groundsill on the plates, we obtain governing equations, boundary conditions, and their force resultants of laminates plates under both hygrothermal environments and elastic groundsill upon higher-order shear deformation theory. Effects of temperature, moisture, elastic coefficients of boundary conditions, elastic parameters of groundsill, and number of laminated plies are studied on the nonlinear bending deflection and moments of composite laminated plates.更多还原