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By Suong Van Hoa, Wei Feng

This publication has one unmarried objective: to give the advance of the partial hybrid finite point procedure for the tension research of laminated composite constructions. the cause of this presentation is as the authors think that partial hybrid finite point process is extra effective that the displacement established finite aspect strategy for the tension research oflaminated composites. actually, the examples in bankruptcy five of this ebook exhibit that the partial hybrid finite aspect approach is set five instances extra effective than the displacement established finite aspect strategy. because there's a nice desire for exact and effective calculation of interlaminar stresses for the layout utilizing composites, the partial hybrid finite procedure does supply one attainable answer. Hybrid finite procedure has been in life considering 1964 and an important volume of labor has been performed at the subject. notwithstanding, the authors aren't conscious of any systematic piece of literature that provides an in depth presentation of the tactic. Chapters of the displacement finite point strategy and the evolution 1 and a couple of current a sununary of the hybrid finite aspect process. expectantly, those chapters promises the readers with an appreciation for the variation among the displacement finite aspect approach and the hybrid finite aspect. It additionally may still organize the readers for the creation of partial hybrid finite aspect process awarded in bankruptcy 3.

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5, p354(1971). B. M. S. Schmidt, '3-D stress analysis of composite plates with or without stress concentrations', Composites Modelling and Processing Science, III, ICCMI9, Ed. Antonio Miravete, Woodhead Publishing Limited, (1993). M. T. R. 2, 1013-1029(1972). 12 M. , 16, 645-650(1983). T. Mau, P. H. Pian, 'Finite element solutions for laminated thick plates', J. 6, 304-311(1972). L. c. Chou and O. Orringer, 'Alternate hybrid-stress elements for analysis of multilayer composite plates', J. 11, 51-70(1977).

Au' ax' au' ay' au' az' av' ax' av' ay' av' az' aw' ax' aw' =[L]T ay' aw' az' au ax au ay au az av ax av ay av az aw ax aw ay aw az [L] (1-68) where [L]=[V,V 2 V 3 ] (1 - 69) V" V 2 and V 3 are three unit normal vectors at a point P based on the direction ~ as a reference. = az' + ay' y' = aw' + au' ax' az' Y xy= X1It Above equation can be put in matrix notation as, (1-70) 29 INTRODUCTION (1-71) Now the element stiffness matrix can be evaluated as [K] +1/+1/+1 -1 -1 [BF] T[C'] [BF] e=/ -1 det [J'] dedTtd{ (1-72) where [C'] is the material constant matrix in the local co-ordinate system.

3-D Solid Element If the displacement field (eq. 1-61) is defined within a layer of laminated composites, the laminated element formulation above becomes a 3-D solid element. 39]. 9]. 41] used 3-D, 20-node solid elements to analyze the cross-ply laminate with a circular hole. Later investigations showed that many elements are required through the thickness of one layer to obtain accurate results. 36] concluded that three linear elements were sufficient when the free-edge effect is studied. 42].

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