New variational-asymptotic formulations for 3-D stress analyses of laminated composite shells with a circular hole

A new approach for three-dimensional stress analyses in composite cylindrical shells is presented. The method of composite expansions along with Hellinger-Reissner variational formulation is employed to derive the interior and edge layer problems for high order approximations. Classical assumptions have been justified and new approximations have been established. These formulations are directed especially towards, new high integrity mixed-hybrid finite element schemes. The expository examples chosen are of cross-ply and angle-ply laminated shells. The circumferential location of the delamination failure initiation, for angle-ply laminates containing a circular hole, is within a sector located symmetrically around the perpendicular direction to the applied load.     

New variational-asymptotic formulations for interlaminar stress analysis in laminated plates

A new approach for the three-dimensional stress analyses in composite laminates is presented. The method of composite expansions along with Hellinger-Reissner variational formulation is employed to derive the interior and edge layer problems for high order approximations. A new method of finite element analysis for solving the edge layer problem is developed based on the modified mixed-hybrid method. Comparison of the present solution with an assumed displacement finite element solution is made to demonstrate the accuracy and efficiency of the present approach.

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Zusammenfassung Eine neue Methode zur dreidimensionalen Spannungsanalyse von Verbundlaminaten wird dargelegt. Die Methode der gewünschten Entwicklungen zusammen mit dem Hellinger-Reissner'schen Variationsprinzip führt zur Herleitung des inneren Problems und des Grenzschichtproblems für höhere Näherungen. Eine neue Methode wird entwickelt, welche mit Hilfe von finiten Elementen, vom gemischt hybriden Verfahren ausgehend, das Grenzschichtproblem löst. Der Vergleich, der hier vorgeschlagenen Lösung mit einer klassischen, auf Verschiebungselementen beruhenden Lösung zeigt die Genauigkeits- und Effizienzvorteile der hier dargelegten neuen Methode.

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This research was supported by Technion V. P. R. fund (grant No. 030-717), New York Metropolitan research fund.