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Determination of the stiffness matrix of flat springs for modeling of the boundary condition at a pipeline support

机译：确定板簧刚度矩阵以建立管道支撑边界条件

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Elastic mounting elements are often used in mechanical systems for reduction of undesired loads. In many engineering applications one-dimensional (1D) approximation of absorber reaction is an acceptable approach however in general, a six order stiffness matrix of an elastic element should be known. This can also be the case of water hammer with fluid-structure interaction in a pipeline fixed with elastic supports. For the standard model of this phenomenon the general boundary condition (BC) at the support should take into account all degrees of freedom of the pipe element. In this paper various methods of flexibility matrix determination of actual, self manufactured flat springs (FS) used as supports at a laboratory pipeline are discussed. Analytical calculations are based on modeling of elastic strain energy of a bar under external loads and formulas being developed for the FS flexibility coefficients are presented. Experimental verification of selected coefficients was performed and the results were consistent with theoretical findings. A general experimental method and a data processing scheme based on linear least squares (LS) method is also proposed and shortly discussed. Numerical investigations are based on FEM modeling of the FS structure and computations of their load-displacement characteristics with the ANSYS software. Flexibility matrix was determined with that same LS data processing scheme. Analytical, experimental and numerical results are compared and discussed. For non-singular flexibility matrix the stiffness matrix used in the BC can be easily determined as its reverse. Otherwise, for a singular case, a special treatment is required. A solution to this problem is developed and presented in the paper. It has been evidenced that singularity results in dimension reduction of the BC. (C) 2019 Elsevier Ltd. All rights reserved.
机译：弹性安装元件通常用于机械系统中，以减少不希望的负载。在许多工程应用中，吸收器反应的一维（1D）近似是可以接受的方法，但是通常，弹性元件的六阶刚度矩阵应该是已知的。水锤在固定有弹性支撑的管道中具有流固耦合也可能是这种情况。对于此现象的标准模型，支座处的一般边界条件（BC）应考虑到管道元件的所有自由度。在本文中，讨论了在实验室管道中用作支撑的实际，自行制造的板簧（FS）的各种挠性矩阵确定方法。分析计算基于外部载荷下钢筋的弹性应变能建模，并给出了为FS挠性系数开发的公式。对所选系数进行了实验验证，结果与理论结果相符。还提出并简要讨论了基于线性最小二乘法的一般实验方法和数据处理方案。数值研究基于FS结构的有限元建模以及使用ANSYS软件计算其载荷-位移特性。使用相同的LS数据处理方案确定灵活性矩阵。对分析，实验和数值结果进行了比较和讨论。对于非奇异的柔韧性矩阵，BC中使用的刚度矩阵可以很容易地确定为相反。否则，对于单个情况，需要特殊处理。本文针对这一问题提出了解决方案。已经证明，奇异性导致BC尺寸减小。 （C）2019 Elsevier Ltd.保留所有权利。

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