利用MLS-Ritz法於預載重下具內部裂縫矩形板之挫曲載重與自然頻率分析

Stability and Vibration Analyses of Preloaded Rectangular Plates with Internal Cracks via MLS-Ritz Method

李旻俊(Min-Chun Lee)

指導教授 ： 黃炯憲

國立交通大學/工學院/土木工程系所/碩士(2016年)

摘要

板在工程應用上，常因為製造過程誤差或者開孔需求而出現裂縫或缺口，此裂縫或缺口存在，當受載重作用下，使得板內出現應力集中與應力重新分配，導致其靜態與動態行為將明顯不同於完整板。本研究係以薄板理論為基礎，利用MLS-Ritz法分析具內部裂縫矩形板受面內載重下之穩定性與振動行為。為提升傳統Ritz法描述局部的物理行為的能力，本研究利用移動最小平方差法(MLS)建構Ritz法之允許函數，並於基底函數中導入能準確描述裂縫尖端處應力奇異性與跨越裂縫之位移與斜率不連續性的裂縫角函數。
本研究為驗證所用方法之可行性與正確性，將收斂性分析所得結果與文獻或ANSYS結果進行比較；最後，利用此法探討不同裂縫長度、裂縫角度、不同之幾何邊界條件與荷重型式下對內部裂縫板之挫屈載重與振動行為的影響。此外，也針對挫屈模態與受面內載重下自然頻率模態形狀圖進行探討。

關鍵字

MLS-Ritz法 ； 古典板理論 ； 薄板理論 ； 應力強度因子 ； 挫屈載重 ； 具內部裂縫矩形板 ； 預載重下之板自然振動頻率

並列摘要

Based on classical thin plate theory, new sets of enriched basis functions for in-plane and out-of-plane displacements are proposed to establish the admissible functions in the Ritz method using the moving least-squares approach. The admissible functions help the Ritz method to recognize the existing of an internal crack in a rectangular plate. The admissible functions display the discontinuities of displacement and slope crossing a crack and give the correct singularity order for the stress resultants at the crack tips. To confirm the validity of the proposed approach, convergence studies on stress intensity factor of plates with central cracks are performed, and the present results are also compared with the previously published results. Besides, convergence studies are performed on the buckling loads and vibrational frequencies of plates with central horizontal cracks, and excellent agreement is found between the present results and the previously published results and the results obtained from commercial finite element software. The effects of different in-plane stress resultant components on the buckling loads of plates with different length cracks under simply supported boundary conditions are investigated to demonstrate the importance of considering all stress resultant components. However, such effects can also depend on loading conditions, boundary conditions and crack configurations and locations. The present approach is further employed to study the effects of crack length, orientation and location on the buckling loads and frequencies of cracked square plates under different boundary conditions and in-plane loading conditions.

並列關鍵字

MLS-Ritz ； stress intensity factor ； buckling load ； frequency ； internal crack thin plate

參考文獻

1. Tong, P., Pian, T.H.H., 1973, On the convergence of the FEM for problems with singularity. International Journal of Solids and Structures 9, 313-321.

2. Belytschko, T., Lu, Y.Y., Gu, L., 1994, Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 37, 229-256.

4. Xiao, Q.Z., Dhanasekar, M., 2002, Coupling of FE and EFG using collocation approach. Advances in Engineering Software 33, 507-515.

5. Hildebrand, G., 2009, Fracture analysis using an enriched meshless method. Meccanica 44, 535-545.

6. Rajesh, K.N., Rao, B.N., 2010, Coupled meshfree and fractal finite element method for mixed mode two-dimensional crack problems. International Journal for Numerical Methods in Engineering 84, 572-609.