利用MLS-Ritz法探討邊緣裂縫對三維彈性方形板之挫屈載重與自然頻率之影響

Abstract

本研究探討邊緣裂縫對三維彈性方形板之挫屈載重與自然頻率之影響。在三維彈性理論下，利用MLS-Ritz法進行分析。所用允許函數是由厚度方向( z )之多項式乘以在x-y平面上以移動最小平方差法配合傳統多項式基底函數及裂縫基底函數建立之允許函數，該裂縫基底函數能準確描述裂縫尖端之應力奇異特性及位移與斜率的跨越裂縫不連續現象。為驗證所提求解方法之正確性，進行一序列收斂性分析並與文獻及利用商業套裝有限元軟體ANSYS所得者比較。 本研究探討不同幾何邊界條件、裂縫長度、傾斜角度、位置、板厚、載重型式對具邊緣裂縫方形板的挫屈載重與自然振動頻率之影響，並繪出挫屈模態與自然振動頻率模態之中平面等高線圖與立體圖。

The main purpose of the study is to apply the MLS-Ritz method to vibrations and buckling of three-dimensional side-cracked square plates. The study proposes new admissible functions to obtain accurate solutions of vibration frequencies and buckling loads for such plates. The proposed admissible functions are constructed by regular polynomial functions in the thickness direction multiplied with the in-plane admissible functions established by the moving least-squares method with a set of enriched basis functions, which consists of crack functions showing the stress singularities at the front of a crack and the displacement discontinuity across the crack. To validate the proposed solutions, comprehensive convergence studies on buckling loads and vibration frequencies are carried out, and some of the results are compared with the published ones and those obtained by commercial finite element software ANSYS. The effects of boundary conditions, loading conditions, plate thickness, cracks’ lengths, orientations, and locations on the buckling loads and vibration frequencies of square plates with side-cracks are fully investigated. The results are tabulated and the vibration and buckling mode shapes are also shown.