- 作者: 劉英偉
- 作者服務機構: 屏東技術學院土木工程技術系與研究所
- 中文摘要: 本文發展一個新的四節點任意四邊形彈性板有限單元之自由振動分析研究,其公式推導係根據Kirchhoff薄板理論與能量正交性理論,可以自動滿足收斂性要求。此彈性板有限單元之幾何外形是由雙線性多項式方程來模擬,其橫向位移函數是經由修正之雙立方曲線來表示,包含了一組基本剛體和等曲率變形模式加上一組高階變形模式。此四節點任意四邊形彈性板有限單元擁有十六個運動自由度,且與橫向位移函數同時建立在卡氏座標系上。同時本文針對典型之板結構實例探討不同之幾何外形效應下以及不規則網格劃分等,比較其差異性與精確性。 本研究不僅可以得到較經濟的四節點任意四邊形板有限單元,亦提供另一套有限單元之自由振動分析模式與方法。
- 英文摘要: The free vibration analysis of general plates using a newly developed four-noded conforming plateelement is presented. The plate formulation is based on the classical Kirchhoff thin plate theory and energyorthogonality theorem and can automatically satisfy the convergence requirements. It employs bilinearfunctions to perform two-dimensional geometric interpolation. The displacement functions are those ofmodified bicubic polynomials which contain a rigid body, constant strain and higher order deformationmodes. The four-noded element has 16 degrees of freedom in total. The displacement functions and degreesof freedom are expressed and investigated in Cartesian form. The numerical results of the new elementare compared with the available data in the literature based on the effects of element geometry and theirregularity of mesh.
- 中文關鍵字: plate finite element; free vibration analysis; energy orthogonality theorem; transverse displacement functions
- 英文關鍵字: --