Shear correction factors for layered plates and shells
Shear correction factors for layered plates and shells
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DOI：
10.1007/s00466-016-1339-2
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发表时间：
2016-10
影响因子：
4.1
通讯作者：
F. Gruttmann;W. Wagner
中科院分区：
文献类型：
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作者：
F. Gruttmann;W. Wagner
本文研究了复合材料层合壳在静载荷作用下的力学行为。该理论是基于一个多场的功能，其中相关的欧拉-拉格朗日方程包括除了制定在应力合成的整体壳方程，局部平面内平衡的应力和约束，强制执行正确的形状翘曲通过厚度。在有代表性的体积单元内，翘曲位移在厚度方向上用逐层三次函数插值，并且在整个参考表面上保持恒定的形状。用静力凝聚法消除翘曲和拉格朗日参数，得到应力合成的材料矩阵和层合板壳的剪切修正系数。对于线弹性，可以预先计算一次。凝聚材料矩阵用于基于位移的单元沿着的增强应变法或用于具有通常的5或6节点自由度的混合杂交单元。这允许标准的几何边界条件和元素也适用于壳相交问题。层间剪应力通过本构关系进行计算，并对已消除的参数进行回代。计算的横向剪应力在层边界自动连续，在外表面为零。此外，剪应力的积分与剪切力完全一致，而无需引入进一步的约束。
In this paper layered composite shells subjected to static loading are considered. The theory is based on a multi-field functional, where the associated Euler–Lagrange equations include besides the global shell equations formulated in stress resultants, the local in-plane equilibrium in terms of stresses and a constraint which enforces the correct shape of warping through the thickness. Within representative volume elements warping displacements are interpolated with layerwise cubic functions in thickness direction and constant shape throughout the reference surface. Elimination of warping and Lagrange parameters by static condensation leads to a material matrix for the stress resultants and to shear correction factors for layered plates and shells. For linear elasticity the computation can be done once in advance. The condensed material matrix is used in displacement based elements along with the enhanced strain method or in mixed hybrid elements with the usual 5 or 6 nodal degrees of freedom. This allows standard geometrical boundary conditions and the elements are applicable also to shell intersection problems. The interlaminar shear stresses are evaluated via the constitutive law by back substitution of the eliminated parameters. The computed transverse shear stresses are automatically continuous at the layer boundaries and zero at the outer surfaces. Furthermore, the integrals of the shear stresses coincide exactly with the shear forces without introduction of further constraints.