STUDY OF THE VIBRATIONS OF MODERATELY THICK DOUBLY CURVED SHELLS VIA EFFICIENT 3D ELEMENTS

Abstract

In this work, we propose a modified version of the classical 20 nodes serendipity element for the dynamic analysis of doubly curved shells. Instead of using the classical strain displacements relations, we propose to formulate the strain displacements relations in a general curvilinear coordinates. The main goal of the work is putting forward a 3D element, valid for general shell structures, which provides some desirable features like avoidance of locking and zero energy modes with decreasing thickness and good behaviour in dynamic analysis. Until now, most works are usually referred to shallow and thin shells. In this work the study of the vibrational frequencies of transverse oscillations of moderately thick shells by 3D elements for non shallow shells has been treated. We expose also different kinds of mass matrices and study a close variant of the classical lumped mass matrix.