Variable kinematic shell elements for composite laminates accounting for hygrothermal effects

Abstract

This paper presents advanced shell models for the steady state hygrothermal analysis of composite laminates. The Carrera Unified Formulation is used to derive refined models that include both Layer-Wise (LW) and Equivalent Single Layer (ESL) models. The governing equations are derived from the Principle of Virtual Displacement (PVD) taking into account thermal and hygroscopic effects. The geometrical relations for the exact cylindrical geometry are here considered. Through-the-thickness variations of temperature and moisture concentration are calculated by solving the Fourier equation and the Fick law, respectively. The Mixed Interpolation of Tensorial Component (MITC) method is applied to a ninenode shell element to contrast the membrane and shear locking phenomena. Simply-supported cross-ply cylindrical shells with anti-symmetrical lamination subjected to bisinusoidal thermal/hygroscopic loads are analyzed considering various thickness/curvature ratios. Results obtained with assumed linear and calculated temperature/hygroscopic profiles are presented. Variable kinematics are compared regarding both accuracy and computational costs. The results show that all the kinematics can approximate the transverse shear stress distribution through the thickness with satisfactory accuracy when sufficient expansion terms are adopted. In some cases, miscellaneous expansions can lead to significant reductions in computational costs. The results here presented can be used as benchmark solutions for future works.

Three-dimensional stress analyses of complex laminated shells with a variable-kinematics continuum shell element

“…where i indexes the finite element nodes, F (•) is a thickness function similar to a Taylor series expansion. Cinefra et al [64] showed that thickness functions based on trigonometric sine, cosine and exponential series are also admissible to model higher-order shear deformation theories. As a second example, a displacement field based on a layer-wise approach can read…”

Buckling Sensitivity of Tow-Steered Plates Subjected to Multiscale Defects by High-Order Finite Elements and Polynomial Chaos Expansion

“…In this manuscript, the Carrera Unified Formulation (CUF) [ 26 ] is utilised for the numerical modelling of VSC plates to exploit its capabilities of creating structural models in which the desired accuracy of the solution is considered as input of the analysis, as demonstrated in [ 27 ]. CUF has been employed for a wide variety of problems such as rotor dynamics [ 28 ], hygrothermal analysis [ 29 ] and incompressible flow analysis [ 30 ]. Moreover, CUF has been recently extended to the study of VSC.…”

Best theory diagrams for multilayered structures via shell finite elements

“…Over the last decades, the research activity has focused on the development of shell and plate models incorporating the effects mentioned above [9,10]. Most recent efforts describe well the open research topics and refinement techniques related to shells, such as, improvements of classical models [11] and higher-order models [12][13][14]; asymptotic approaches [15]; improvement of FE performances regarding membrane and shear locking [16][17][18][19][20][21], mesh accuracy [22], and distortion [23]; improved modeling of the interlaminar shear stresses [24]; Layer-Wise (LW) models [25,26]; Zig-Zag models [27,28]; mixed formulations [29][30][31]; variable kinematics finite elements with multifield effects [32]; extensions to non-linear problems [33,34] and peridynamics [35]; innovative solution schemes such as the numerical manifold method [36].…”