Abstract
本論文主要發展複合式應力有限單元分析模式，配合接觸力學分析程序，研究複材疊層板與剛性球體間三維無摩擦接觸問題。由於複合式應力有限單元分析中，未知參數和自由度均與層數無關，且接觸面滿足幾何諧合條件，適合用以處理複材疊層板與剛性球體間三維無摩擦接觸問題。經由實例解析，證實了本分析方法的正確性與適用性。對於疊層效應，球體直徑效應，跨距效應及邊界效應對凹陷律的影響，亦做詳細的探討。A hybrid stress multilayer element model together with thecontact mechanics analysis procedure are developed to study thethree dimensional frictionless contact problem between ageneral composite laminate and a rigid sphere. The multilayerelement model is formulated based on a modefied complementaryenergy priciple. To relax the equilibrium of interelementtractions, in addition to the stress field in the interior ofthe element, the Lagrangian multipliers which are physicallythe interelement boundary displacements are introduced and theinterelement traction reciprocity and mechanical boundaryconditions are satisfied. Besides, in the multilayer elementsmodel, the undetermined stress parameters and total degrees offreedom are independent of the number of layers and thekinematic conditions are satisfied on the ntact surfaces.Hence, the application of the present techique has no limiationof the geometry, stacking arrangement, boundary conditions andnumber of layers. The contact problem of a general graphite/epoxy laminate and a rigid sphere is solved. Excellentagreements between the present result andference solutions showthe high accuracy and validity of the technique developed. Theeffects of sphere diamenter, stacking arrangement, span andboundary conditions on the indentation law are also disscussedin details.