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首页> 外文期刊>Mathematical Problems in Engineering >Dynamic Stationary Response of Reinforced Plates by the Boundary Element Method
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Dynamic Stationary Response of Reinforced Plates by the Boundary Element Method

机译：边界元法对加筋板的动态平稳响应

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摘要

A direct version of the boundary element method (BEM) is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs). Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state (membrane) and for the out-of-plane state (bending). These uncoupled systems are joined to form a macro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corresponding mode shapes of reinforced plates, are obtained from information contained in the frequency response functions (FRFs). A specific example is presented to illustrate the versatility of the proposed methodology. Different configurations of the reinforcements are used to simulate simply supported and clamped boundary conditions for the plate structures. The procedure is validated by comparison with results determined by the finite element method (FEM).
机译：开发了边界元方法（BEM）的直接版本来对增强板结构（例如建筑物，汽车和飞机中的增强板）的静态动力响应进行建模。利用薄板的动态平稳基本解和平面应力状态将控制性偏微分方程转换为边界积分方程（BIE）。分别针对面内状态（膜）和面外状态（弯曲）制定了两组未耦合的BIE。将这些未耦合的系统连接起来以形成一个宏观元素，其中存在膜效应和弯曲效应。这些宏元素的关联能够模拟薄壁结构，包括增强板结构。在本配方中，BIE通过连续和/或不连续的线性元素离散化。为每个边界节点编写四个位移积分方程。从频率响应函数（FRF）中包含的信息中获取模态数据，即固有频率和增强板的相应模态形状。给出了一个具体的例子来说明所提出方法的多功能性。增强件的不同配置用于模拟板结构的简单支撑和夹紧边界条件。通过与有限元方法（FEM）确定的结果进行比较来验证该过程。

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