A novel finite element for the vibration analysis of tapered laminated plates

Abstract

AbstractIn the present study, a new tapered finite element is developed by incorporating the in‐plane effect in our recently introduced element for the vibration analysis of internally tapered laminated plates. Stress and strain fields for a laminated plate with varying thickness along two orthogonal directions are expressed through extending classical laminated plate theory. Shape functions regarding bending and membrane behavior are extracted from the bending and axial basic displacement functions of the Euler‐Bernoulli beam, respectively. Several laminated plates with different taper configurations have been studied, and the results obtained from vibration analysis are compared with those of the literature. Since the element can capture the exact form of variation in thickness, the solution has shown to be competitively accurate with considerably fewer total degrees of freedom and elements in comparison with conventional finite elements.Highlight A new finite element for thin, tapered, laminated plates is introduced. Laminates' stiffness matrix is obtained for arbitrary thickness variation. A novel method is adopted to derive in‐plane shape functions. C1 continuity is guaranteed along the edges of elements. Calculation cost is considerably reduced.