Elastic stability of skew laminated composite plates subjected to biaxial follower forces

Abstract

SUMMARYThe present study investigates the elastic stability of skew laminated composite plates subjected to biaxial inplane follower forces by the finite element method. The plate is assumed to follow first-order shear deformation plate theory (FSDPT). The kinetic and strain energies of skew laminated composite plate and the work done by the biaxial inplane follower forces are derived by using tensor theory. Then, by Hamilton's principle, the dynamic mathematical model to describe the free vibration of this problem is formed. The finite element method and the isoparametric element are utilized to discretize the continuous system and to obtain the characteristic equations of the present problem. Finally, natural vibration frequencies, buckling loads (also the instability types) and their corresponding mode shapes are found by solving the characteristic equations. Numerical results are presented to demonstrate the effects of those parameters, such as various inplane force combinations, skew angle and lamination scheme, on the elastic stability of skew laminated composite plates subjected to biaxial inplane follower forces.

Large amplitude free flexural vibrations of laminated composite skew plates

“…Here, 1 ( 1 r; 2 r) and 2 ( 1 r; 2 r) are the total rotations; 1 ( 1 r; 2 r) and 2 ( 1 r; 2 r) are the rotations due to shear deformation of the normal to the plate middle surface around 2 g axis and 1 g axis respectively; ( ) ;i represents the partial di erentiation of the variable preceding it with respect i r. Now the covariant components of strain tensor ( = ij i g j g) can be written in terms of displacement components u (u = u i i g = k ug k ) as [27,29] ij = 1 2 (u i; j + u j; i + k u ;i u k; j ):…”

Geometrically nonlinear bending of stiffened composite skewed cylindrical shells under transverse pressure

“…However, those were conducted on plates only. Liao and Lee 13 worked on elastic stability of plates. A hybrid/mixed finite element method was employed by Duan and Mahendran 14 to investigate deflections of skewed plates.…”

Flutter instability of damped plates under combined conservative and nonconservative loads

“…The finite element method was called into the arena to treat real engineering problems. Liao and Lee [22] used the FEM to examine skew laminated plates subjected to follower forces. Kim et al [23,24] also used the FEM to analyze Kirchhoff and Mindlin plates under follower forces.…”