摘要 : The static response of beams constructed of graphite--epoxy and piezoelectric laminate (hybrid laminate) subjected to electric field and thermal (i.e. self-strained) loading is considered. Two theoretical formulations are consider... 展开 The static response of beams constructed of graphite--epoxy and piezoelectric laminate (hybrid laminate) subjected to electric field and thermal (i.e. self-strained) loading is considered. Two theoretical formulations are considered: uncoupled which ignores the 'direct piezo- electric effect' (induced electric field due to variation in stress), and 'coupled' which includes the direct piezoelectric effect. A hierarchical finite element approximation of the governing equations using reduced material stiffness coefficients is developed. The electromagnetic potential is assumed to vary piecewise linearly through each piezoelectric lamina and the lamina surface that is in contact with a structural lamina is assumed to be grounded. Beam displacement theory is based on Reissner--Mindlin shear deformation theory. Sample problems are presented demonstrating the accuracy of the developed finite element model, and the response of hybrid laminates to self-strained loading. 收起