• 대한기계학회논문집A
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• 제27권2호
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• pp.302-309
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• 2003

Hybrid-Trefftz plate bending elements are known to be robust and free of shear locking in the thin limit because of Internal displacements fields and linked boundary displacements. Also, their finite element approximation is very simple regardless to boundary shape since all element matrices can be calculated using only boundary integrals. In this study, new hybrid-Trefftz variational formulation based on the total potential energy principle of internal displacements and displacement consistency conditions at the boundary is derived. And flat shell elements are derived by combining hybrid-Trefftz bending stiffness and plane stress stiffness with drilling dofs.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2004년도 추계학술대회 논문집
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• pp.855-859
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• 2004

We develop a new four-node flat shell element which is accurate, efficient, and suitable to be used on general purpose. The new element has a hybrid Trefftz element with drilling degrees of freedom as a membrane part. We define the two independent displacement field: the internal displacement field that satisfies governing equations in the domain a priori and the boundary displacement field that is usually used as a conventional finite element method. The hybrid Trefftz variational formulation connects these two displacement fields on the boundary of the domain. To add drilling degrees of freedom, we introduce the Allman's quadratic displacement field to the boundary displacement field. As a result, our flat shell element has 6 degrees of freedom per a node. We also use the well-known DKMQ plate bending element for the plate part of the proposed element. The DKMQ element satisfies Mindlin-Reissner‘s plate theory along the edge of the element and gives proper behavior regardless of the thickness. A series of numerical experiments shows that the performance of the new element such as accuracy, rate of convergence, robustness to mesh quality, and so on.