Analyzing FG shells with large deformations and finite rotations

Abstract

Purpose The purpose of this study is dedicated to use an efficient mixed strain finite element approach to develop a three-node triangular shell element. Moreover, large deformation analysis of the functionally graded material shells is the main contribution of this research. These target structures include thin or moderately thick panels. Design/methodology/approach Due to reach these goals, Green–Lagrange strain formulation with respect to small strains and large deformations with finite rotations is used. First, an efficient three-node triangular degenerated shell element is formulated using tensorial components of two-dimensional shell theory. Then, the variation of Young’s modulus through the thickness of shell is formulated by using power function. Note that the change of Poisson’s ratio is ignored. Finally, the governing linearized incremental relation was iteratively solved using a high potential nonlinear solution method entitled generalized displacement control. Findings Some well-known problems are solved to validate the proposed formulations. The suggested triangular shell element can obtain the exact responses of functionally graded (FG) shell structures, without any shear locking, instabilities and ill-conditioning, even by using fewer numbers of the elements. The obtained outcomes are compared with the other reference solutions. All findings demonstrate the accuracy and capability of authors’ element for analyzing FG shell structures. Research limitations/implications A mixed strain finite element approach is used for nonlinear analysis of FG shells. These structures are curved thin and moderately thick shells. Small strains and large deformations with finite rotations are assumed. Practical implications FG shells are mostly made curved thin or moderately thick, and these structures have a lot of applications in the civil and mechanical engineering. Social implications The social implication of this study is concerned with how technology impacts the world. In short, the presented scheme can improve structural analysis ways. Originality/value Developing an efficient three-node triangular element, for geometrically nonlinear analysis of FG doubly-curved thin and moderately thick shells, is the main contribution of the current research. Finite rotations are considered by using the Taylor’s expansion of the rotation matrix. Mixed interpolation of strain fields is used to alleviate the locking phenomena. Using fewer numbers of shell elements with fewer numbers of degrees of freedom can reduce the computational costs and errors significantly.

Vibration Characteristics of a Functionally Graded Viscoelastic Fluid-Conveying Pipe with Initial Geometric Defects under Thermal–Magnetic Coupling Fields

“…Xu et al [15] studied the vibration responses and dynamic characteristics of functionally graded cylinders and imperfect microbeams under dynamic harmonic loads. Rezaiee-Pajand and Masoodi [16,17] examined conical beams and columns with a functional classification of the cross-section, verified the effectiveness of the stiffness matrix, and provided an effective calculation unit for the study of functionally graded material shells. Masoodi and Ghandehari [18] studied the dynamic characteristics of functionally graded single-wall carbon nanocoupled curved beams and analyzed the effects of factors such as curvature and interface stiffness on the vibration characteristics of the system.…”

Numerical Investigation on Blast Response of Cold-Formed Steel Framing Protected with Functionally Graded Composite Material

“…Their research found out that steel stud walls constructed using conventional detailing have limited blast resistance due to premature buckling instability. A non-linear analysis of FGM sandwich plates and shell, as well as FGM large deformation analysis, is presented in [11][12][13][14]. Similar articles on FGM and resistance of steel wall systems can also be found in several studies [15][16][17][18][19][20][21][22].…”

Buckling and Post-Buckling Behavior of Perfect/Perforated Composite Cylindrical Shells under Hydrostatic Pressure

“…Mohammad [18] employed a triangular shell element having six nodes to investigate the nonlinear behavior of cylindrical shells with irregular mesh and complicated geometry, where total Lagrangian formulation was utilized considering the large deflection and rotation. Further, Mohammad [19] developed a three-node triangular shell element using a mixed strain finite element approach for nonlinear analysis of FG shells with large deformations and finite rotations. For composite cylindrical shells of given geometry, boundary conditions and material system, the buckling strength is mainly affected by the fiber orientation, stacking sequence and thermal environment [20][21][22][23][24][25].…”