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End Effects in Prestressed Plates under Compression

机译:压缩下预应力板的最终效果

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The decay of end perturbations imposed on a rectangular plate subjected to compression is investigated in the context of plane-strain incremental finite elasticity. A separation of variables in the eigenfunction formulation is used for the perturbed field within the plate. Numerical results for the leading decay exponent are given for compressible foamed rubber modeled by hyperelastic Blatz-Ko material. It was found that the lowest decay rate is governed by a symmetric field that exposes relatively low sensitivity to compressive strain in a low regime of pre-strain. Under such circumstances, the values for decay rate obtained from linear elastic analysis can be considered as a good approximation for a slightly compressed plate. For higher compressive pre-strain levels, the decay distance increases significantly. Along with decaying modes representing end effects, the eigenfunction expansion generates a non-decaying anti-symmetric mode corresponding to buckling of the plate. It is remarkable that asymptotic expansion of that non-decaying mode predicts buckling according to the classical Euler formula.
机译:在平面 - 应变增量有限弹性的背景下研究了对经受压缩的矩形板上施加的矩形扰动的衰减。特征函数制剂中的变量的分离用于板内的扰动场。给出了由超弹性Blatz-KO材料建模的可压缩泡沫橡胶给出的前导衰减指数的数值结果。结果发现,最低衰减率由对称场管辖,对称领域对对菌株的低制度处的压缩应变暴露相对较低的灵敏度。在这种情况下,从线性弹性分析获得的衰减率的值可以被认为是略微压缩板的良好近似。对于更高的压缩预抑制级别,衰减距离显着增加。随着代表终结的衰减模式,特征函数扩展产生对应于板的弯曲的非腐朽的反对称模式。值得注意的是,这种非腐朽模式的渐近扩展预测根据经典欧拉公式的屈曲。

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