GENERALIZED LAMINATE THEORIES BASED ON DOUBLE SUPERPOSITION HYPOTHESIS

There was a tremendous advantage of using the generalized co-ordinate system to express various types of laminate theories. With two layer-dependent terms of both the zeroth- and the Þrst-order of thickness co-ordinate, a generalized zigzag theory was presented in a previous study. Due to its success in laminate analysis, the feasibility of assigning the two high-order terms, i.e. the second- and the third-order terms, of the generalized zigzag theory as layer-dependent variables was of primary interest. It was found that a so-called globalÐlocal superposition technique could be used for expressing the laminate theories in an explicit manner, namely recursive equations, to retain the advantage of numerical e¦ciency. Based on the superposition technique, the fundamental roles of the individual terms are identiÞed. It is concluded that not only the completeness of the terms, but also the inclusion of as many terms as possible, is important to a laminate theory. It then is the goal of this study to look into a laminate theory which can satisfy the requirement of completeness and include all the Þrst-, second- and third-order terms in an assumed displacement Þeld. A special technique, namely hypothesis for double superposition, is presented to achieve the goal. The feasibility of the hypothesis is demonstrated in this study. Although not veriÞed mathematically, the hypothesis seems to be capable of giving accurate and e¦cient laminate theories