Smoothed finite element approach for viscoelastic behaviors of general shell structures

This study focuses on the viscoelastic analysis of laminated composite shell structures under long-term creep mechanical loading. An advanced finite element technique named as cell/element-based smoothed discrete shear gap method (CS-DSG3) is employed to obtain the numerical solutions for both elastic and viscoelastic problems owing to its accuracy and rapid convergence. In the CS-DSG3 shell element, each triangular shell element is divided into three DSG3 subtriangles to avoid transverse shear locking. Subsequently, the total element strain is computed from the three partial strains of the subtriangles using a smoothing technique. To overcome the difficulty in the constitutive equations in integral forms for a viscoelastic material, all formulations are transformed into the Laplace domain using the convolution theorem. Finally, time-dependent deformations are obtained and converted back to the real-time domain using inverse Laplace techniques. For validation, various numerical examples of a pinched cylinder, clamped hyperbolic paraboloid, and hemispherical shell formed of isotropic elastic, isotropic viscoelastic, and anisotropic composite materials are selected to investigate creep behavior under mechanical loading. The present study extends the finite element simulation of anisotropic viscoelastic shell structures to achieve high accuracy and efficiency based on the Laplace transform and CS-DSG3.