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所在平台: Udemy |
课程主页: https://www.udemy.com/course/theory-of-plates/
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**课程名称：板壳理论 (Theory of Plates)** **课程概述：** 本课程深入探讨板壳理论的核心概念，涵盖了板的弯曲理论、矩形板和圆形板的分析方法、能量法以及数值方法。 **课程目标：** * 掌握板的平衡微分方程，并将其应用于求解不同边界条件下矩形板的纯弯曲和圆筒弯曲问题。 * 掌握求解对称弯曲圆形板平衡微分方程的方法，以分析各种载荷作用下的圆形板。 * 计算简单支承矩形板在单轴或双轴受压作用下，不同边缘条件下的临界载荷与屈曲模式。 * 运用Navier法和Levy法求解简单支承矩形板在各种载荷作用下的挠度和应力分布。 * 掌握有限差分法，用于求解简单支承或固定矩形板在不同载荷作用下的挠度和应力分布。 **课程内容要点：** * **矩形板弯曲：** * 纯弯曲与圆筒弯曲 * 弯曲微分方程 * 均布荷载下简单支承和固定边缘矩形板的圆筒弯曲 * 微小弯曲板的斜率与曲率关系 * 纯弯曲中的弯矩-曲率关系 * 纯弯曲中的应变能 * **圆形板弯曲：** * 对称弯曲 * 平衡微分方程 * 中心受均布荷载的圆形板 * 中心带圆形孔的圆形板 * **板屈曲：** * 在平面内和横向载荷联合作用下板的屈曲微分方程 * 临界载荷的计算 * 在单向或双向均匀受压作用下，不同边缘条件下的简单支承矩形板的屈曲 * **横向荷载作用下板的小挠度：** * 平衡微分方程 * 边界条件 * Navier法求解简单支承矩形板在各种载荷（均匀分布、局部均布、集中力）下的解 * Levy法求解四边简单支承或两边简单支承、两边固定的矩形板在均布荷载下的解 * **矩形板的近似方法：** * 简单支承或固定矩形板在均布荷载（全或局部）或中心点荷载作用下的有限差分法 * Rayleigh-Ritz法的应变能方法
This course deals with the theory of plate bending; rectangular and circular plates; energy methods and numerical method. The course objectives are:To apply the differential equation of equilibrium to solve problems of pure and cylindrical bending of rectangular plates with different boundary conditions.To solve the differential equation of equilibrium for symmetrical bending of circular plates under various loading conditions.To determine the critical loads and buckling modes for simply supported rectangular plates under uniaxial or biaxial compression with different edge conditions.To apply the Navier's approach and Levy type solution to find the deflection and stress distribution for simply supported rectangular plates under various loading conditions.To use the finite difference method to solve for the deflection and stress distribution for simply supported or fixed rectangular plates under different loading conditions.Bending of Rectangular Plates: Pure and Cylindrical bending, differential equation, cylindrical bending of uniformly loaded rectangular plates with simply supported and built-in edges. Relations between slope and curvature of slightly bent plates, Moment-curvature relations in pure bending. Strain energy in pure bending.Bending of circular plates: Symmetrical bending, differential equation of equilibrium, uniformly loaded plates at center, Circular plates with circular holes at the center.Buckling of Plates: Differential equation for bending of plate under the combined action of in-plane loading and lateral loading, Calculation of critical loads, buckling of simply supported rectangular plates uniformly compressed in one and two directions with different edge conditions.Small deflections of laterally loaded plates: Differential equation of equilibrium, Boundary conditions, Solution of simply supported rectangular plates under various loading conditions viz. uniformly distributed load (full or partial), concentrated load by Navier's approach, Levy type solution for rectangular plates under U.D.L with all four edges simply supported or two opposite edges simply supported and other two fixed.Approximate methods for Rectangular Plates: Finite difference method for simply supported or fixed rectangular plates carrying UDL (full or partial) or central point load, Strain energy approaches Rayleigh-Ritz method.
