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首页> 外文会议>Advances in Computational Methods in Sciences and Engineering 2005 vol.4A; Lecture Series on Computer and Computational Sciences; vol.4A >A New Approach in Cell Centred Finite Volume Formulation for Plate Bending Analysis
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A New Approach in Cell Centred Finite Volume Formulation for Plate Bending Analysis

机译：用于板弯曲分析的单元中心有限体积公式化的新方法

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摘要

In this paper a novel approach is developed in the application of cell centred finite volume method for plate bending analysis. The essence of this new approach lies in the use of interim elements and evaluating derivatives of unknown variables using the natural coordinate system of the interim elements. Mindlin-Reissner plate theory is applied in which the lateral shear effects are taken into account. The plate is meshed by elements that have arbitrary number of sides. These multi-faced elements are considered as control volumes or cells. The conservation of resultant forces, equilibrium equations, is written in the discretized form for the each cell. To evaluate the resultant forces on the faces of the cell, in the equilibrium equations, a 4-node interim element is used that enclosed the face. The interim element is isoparametric and its vertices are the centres of the two adjacent cells lying on either side of the face and the nodes at each end of the face. Shape functions are used to interpolate the unknown variables in the interim elements, and hence across the enclosed faces. The interpolation functions are defined in the natural coordinate system of the interim element. The derivative of unknown variables is evaluated in the natural coordinate of the interim element and then mapped back to global coordinate system. The equilibrium equations of a cell are approximated at the integration points, which are located in the interim elements. In this approach stress continuity will be guaranteed on common faces of the adjacent cells, which is a prominent feature of the finite volume method. To incorporate the boundary conditions point cells are used to transfer the boundary conditions to the adjacent cells. To demonstrate the capability of the present method in the predictions of accurate results a thin plate is analyzed and the results are compared with the analytical predictions. Further studies of the present method show the formulation is capable to analyze thin and thick plates. It is noticeable that the formulation does not show shear locking problem in the thin plate analysis, which occurs in the Mindlin based finite element formulation for the thin plate analysis. This extended studies cannot be included in this paper regards to the paper length.
机译：本文提出了一种新的方法，将单元中心有限体积方法应用于板弯曲分析。这种新方法的本质在于使用临时元素，并使用临时元素的自然坐标系评估未知变量的导数。应用Mindlin-Reissner板理论，其中考虑了横向剪切效应。板由具有任意多个边的元素划分网格。这些多方面的元素被视为控制体积或单元。对于每个单元，合力守恒，平衡方程以离散形式写出。为了评估单元表面上的合力，在平衡方程中，使用了一个四节点的临时元素将其围住。临时元素是等参的，其顶点是位于该面两侧的两个相邻像元的中心以及该面两端的节点。形状函数用于对临时元素中的未知变量进行插值，从而对封闭面进行插值。插值函数在临时元素的自然坐标系中定义。在临时元素的自然坐标中评估未知变量的导数，然后将其映射回全局坐标系。单元的平衡方程在位于过渡元素中的积分点处近似。在这种方法中，将确保相邻单元的公共面上的应力连续性，这是有限体积法的一个突出特征。为了合并边界条件，使用点像元将边界条件传递到相邻像元。为了证明本方法在准确结果预测中的能力，对一块薄板进行了分析，并将结果与​​分析预测进行了比较。本方法的进一步研究表明该制剂能够分析薄板和厚板。值得注意的是，该配方在薄板分析中没有显示剪切锁定问题，这在基于Mindlin的薄板分析有限元配方中出现。关于纸张长度，本文不能包括这种扩展的研究。

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