基於高階板理論,本文探討雙模數積層板之有限元素法挫屈分析。由於雙模數複合材料性質具有不同的伸張和壓縮彈性模數,因而中性面不固定於板幾何中面上,其需以疊代法求之。本文探討挫屈荷載為沿板厚度方向為等值的均佈同面應力,因而相對應的薄膜應變可完整地表現高階板理論之非線性位移場對臨界挫屈荷載的效果。經由擾動的觀念,推導得有限元素法控制方程式,於具有不同模數比及寬厚比之雙模數層板臨界挫屈荷載之實例分析中,得到與理論解非常接近的結果,故可證實本文所發展的有限元素法之精確性與適用性。
In this paper, a higher-order plate element has been developed to analyze the critical buckling loads of the bimodulus laminates. The bimodular material exhibits load- dependent elastic properties, i. e. the tensile Young's modulus is different from the compressive modulus. It makes the behaviour of bimodulus laminates a nonlinear problem. Therefore, the neutral plane of the plate is not fixed in the midplane surface. The neutral surface is then determined by the iterative method herein. An uniform in-plane stresses are assumed distributed through the thickness in the buckling analysis. Through the purtabation technique, the governing finite element equations for the stability analysis becomes a generalized eigenvalue problem. To demonstrate the accuracy and efficiency of the present study, several benchmark problems are illustrated. Simple-supported square laminates of different span-to-width ratios and modulus ratios are investigated. The locations of neutral surfaces and the critical buckling loads are evaluated. Compared to the analytical solutions, excellent results and fast convergence are observed.
