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A fourth-order finite volume method for structural analysis

机译：结构分析的四阶有限体积方法

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摘要

A fourth-order finite volume method for linear-elastic solid body stress analysis is presented. To demonstrate the method's shear-locking-free behaviour, the discretisation is performed on 2D uniform Cartesian grids. The terms resulting from the fourth-order discretisation that involve an extended computational molecule are treated explicitly in a deferred correction manner, and the coefficients are calculated using a second-order discretisation, thus maintaining a compact computational molecule involving only the nearest neighbours. First, a number of simple test cases are designed to show that the method is exact for any polynomial up to the third order. After that, a beam subjected to thermal stresses and a cantilever fixed at one and loaded at the other end, for which analytical solutions exist, are analysed. In both latter cases, the method produces the exact analytical solution even on the coarsest grids. The fourth-order method results are compared with results obtained with a second-order method.
机译：提出了线性弹性固体应力分析的四阶有限体积方法。为了证明该方法的无剪切锁定行为，在2D统一的笛卡尔网格上进行离散化。涉及扩展计算分子的四阶离散化所产生的术语将以递延校正方式进行显式处理，并使用二阶离散化来计算系数，从而保持仅涉及最近邻的紧凑计算分子。首先，设计了许多简单的测试用例，以证明该方法对于任何三阶以下的多项式都是正确的。此后，分析受到热应力作用的梁和固定在一端并在另一端加载的悬臂，为此存在分析解决方案。在后两种情况下，即使在最粗糙的网格上，该方法也能产生精确的解析解。将四阶方法的结果与二阶方法获得的结果进行比较。

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