頁籤選單縮合
題 名 | A Simple Method for Derivation of the Geometrical Stiffness Matrix of a Frame Element by Rigid-Body Rotation Concept |
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作 者 | 張健財; 黃依典; | 書刊名 | 萬能學報 |
卷 期 | 24 2002.08[民91.08] |
頁 次 | 頁115-127 |
分類號 | 440 |
關鍵詞 | |
語 文 | 英文(English) |
英文摘要 | The derivations and applications of the geometric nonlinear frame elements have attracted many researchers during the past three decades, most of the coefficients existing in the geometric stiffness matrix of the nonlinear frame element by the theoretic formulations are always lengthy and tedious in the expressions. In this study, a method being simple and easy is proposed in the formulations of the geometric stiffness matrix. Based on physically intuitive thought, the geometric stiffness matrix of a frame element is derived. The simple ideas can be stated as: once an element is in equilibrium under a set of initial forces acted, while it is under the rigid body motions, the forces acted upon it would keep their magnitudes and rotate with the rigid body rotations. It is named as rigid body rule. This physical phenomenon corresponds to the invariant nature of stress measured by second Piola-Kirchhoff stree and Green-Lagrange strain under rigid body displacement fields. Based on the ideas of the rigid body motions, a geometric stiffness matrix being simple and explicit can be established easily. When it is combined with linear elements, a simple and useful geometric nonlinear frame element is established. It is a frame element with two nodes, each nodal with six degrees of freedom. Then it is used to conduct geometric nonlinear analysis. A good solution is always obtainable under a little mesh refinement in the nonlinear analyses of the structures. Here, the load-deflection curve of the structure will be traced by the general displacement control method. By the example demonstrated, it ensures that this study is a useful and it provides an easy method for engineers to derive the geometric stiffness matrix of a frame element. |
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