MITC9 shell finite elements with miscellaneous through-the-thickness functions for the analysis of laminated structures

Adv. Model. and Simul. in Eng. Sci.

et al. 2019

Shear and membrane locking phenomena are fundamental issues of shell finite element models. A family of refined shell elements for laminated structures has been developed in the framework of Carrera Unified Formulation, including hierarchical elements based on higher-order Legendre polynomial expansions. These hierarchical elements were reported to be relatively less prone to locking phenomena, yet an exhaustive evaluation of them regarding the mitigation of shear and membrane locking on laminated shells is still essential. In the present article, numerically efficient integration schemes for hierarchical elements, including also reduced and selective integration procedures, are discussed and evaluated through single-element p-version finite element models. Both shear and membrane locking are assessed quantitatively through the estimation of strain energy components. The numerical results show that the fully integrated hierarchical shell elements can overcome the shear and membrane locking effectively when a sufficiently high polynomial degree is reached. Reduced and selective integration schemes can help with the mitigation of locking on lower-order hierarchical shell elements.

Section: Carrera Unified Formulation (Cuf) For Refined 2d Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Evaluation of shear and membrane locking in refined hierarchical shell finite elements for laminated structures

Carrera

Adv. Model. and Simul. in Eng. Sci.

et al. 2019

“…Such an MITC shell element with a variety of thickness functions have been used to investigate the static response of cross-ply laminated plates and shells [41].…”

Section: Introductionmentioning

confidence: 99%

Variable kinematic shell elements for composite laminates accounting for hygrothermal effects

Journal of Thermal Stresses

Petrolo

et al. 2017

Self Cite

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.

“…The Mixed Interpolation of Tensorial Components (MITC) [30][31][32][33] method was implemented to alleviate lockings. Such an MITC9 element with a variety of thickness functions have been used to investigate the static response of cross-ply laminated plates and shells [34].…”

Section: Introductionmentioning

confidence: 99%

Hygrothermal analysis of multilayered composite plates by variable kinematic finite elements

Journal of Thermal Stresses

Petrolo

et al. 2017

Self Cite

Advanced plate models with variable kinematics for steady state hygrothermal analysis of composite laminates are proposed. The refined models discussed include both Layer-Wise (LW) and Equivalent Single Layer (ESL) models, and the Carrera Unified Formulation (CUF) is used. The Mixed Interpolation of Tensorial Component (MITC) method is applied to a nine-node element to contrast the shear locking phenomena. The governing equations are derived from the Principle of Virtual Displacement (PVD) taking into account elastic mechanical, thermal and hygroscopic effects. Through-the-thickness variations of temperature and moisture concentration are calculated by solving the Fourier equation and the Fick law, respectively. Cross-ply plates with symmetrical lamination and simply supported edges subjected to bisinusoidal thermal/hygroscopic loads are analyzed considering various thickness ratios. Results obtained with assumed linear and calculated temperature/hygroscopic profiles are compared. Variable kinematics with a variety of thickness functions are compared regarding both accuracy and computational costs. The results show that all the kinematics proposed 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.