An effective meshfree reproducing kernel method for buckling analysis of cylindrical shells with and without cutouts
An effective meshfree reproducing kernel method for buckling analysis of cylindrical shells with and without cutouts
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DOI：
10.1007/s00466-017-1384-5
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发表时间：
2017-02
影响因子：
4.1
通讯作者：
S. Sadamoto;M. Ozdemir;S. Tanaka;K. Taniguchi;T. Yu;T. Bui
中科院分区：
文献类型：
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作者：
S. Sadamoto;M. Ozdemir;S. Tanaka;K. Taniguchi;T. Yu;T. Bui
本文用一种有效的无网格法分析了有开孔和无开孔曲壳的特征屈曲。特别考虑了扁壳、圆柱体和开孔圆柱体的屈曲问题。然后提出了一种伽辽金无网格再生核(RK)方法。本文的无网格曲壳模型基于Reissner-Mindlin板列式，允许曲壳的横向剪切变形。每个节点有五个自由度(即三个位移和两个旋转)。在此设置中，无网格插值函数是从RK派生的。由于RK形函数不自动具有Kronecker Delta性质，引入了奇异核来施加本质边界条件。利用稳定化协调节点积分技术推导了结构的刚度矩阵。在公式中引入随体坐标系来处理曲线曲面。更重要的是，这里的RKS不仅用于曲面几何的插补，而且还用于场变量的逼近。用无网格法计算了扁壳和满圆柱体模型的临界屈曲载荷及其屈曲振型，并对其进行了检验。为了验证无网格法的精度和性能，将计算的临界屈曲载荷和振型与基于边界元、有限元和解析法的参考解进行了比较。
The paper is concerned with eigen buckling analysis of curvilinear shells with and without cutouts by an effective meshfree method. In particular, shallow shell, cylinder and perforated cylinder buckling problems are considered. A Galerkin meshfree reproducing kernel (RK) approach is then developed. The present meshfree curvilinear shell model is based on Reissner-Mindlin plate formulation, which allows the transverse shear deformation of the curved shells. There are five degrees of freedom per node (i.e., three displacements and two rotations). In this setting, the meshfree interpolation functions are derived from the RK. A singular kernel is introduced to impose the essential boundary conditions because of the RK shape functions, which do not automatically possess the Kronecker delta property. The stiffness matrix is derived using the stabilized conforming nodal integration technique. A convected coordinate system is introduced into the formulation to deal with the curvilinear surface. More importantly, the RKs taken here are used not only for the interpolation of the curved geometry, but also for the approximation of field variables. Several numerical examples with shallow shells and full cylinder models are considered, and the critical buckling loads and their buckling mode shapes are calculated by the meshfree eigenvalue analysis and examined. To show the accuracy and performance of the developed meshfree method, the computed critical buckling loads and mode shapes are compared with reference solutions based on boundary domain element, finite element and analytical methods.