P-Version axisymmetric shell element for geometrically nonlinear analysis

Three-dimensional curved beam element based on p-Version for dynamics

formula omitted] piecewise hierarchical axisymmetric shell element for heat conduction in laminated composites

A three node two-dimensional laminated composite curved beam finite element formulation for linear static analysis is presented where the displacement approximation for the laminate is piecewise hierarchical and is derived based on p-version. The displacement approximation for the element is developed by establishing a hierarchical displacement approximation for each lamina of the laminate and then by imposing interlamina continuity conditions of displacement at the interfaces between the laminas. The approximation functions and the nodal variables for each lamina are derived directly from the Lagrange family of interpolation functions of order pξand pη. This is accomplished by first establishing one-dimensional hierarchical approximation functions and the corresponding nodal variable operators in the ξ and η directions for the three and one node equivalent configurations that correspond to pξ+1 and pη+1 equally spaced nodes in the ξ and η directions and then taking their products. The nodal variables for the entire laminate are derived from the nodal variables of the laminas and the interlamina continuity conditions of displacements. The element formulation ensures C0 continuity of displacement across the interelement as well as interlamina boundaries.

p-Approximation axisymmetric shell elements for heat conduction in laminated composites

Completely hierarchical two-dimensional curved beam element for dynamics

Corresponding relationships between certain incremental equilibrium equations and compatibility equations can be derived for structures undergoing gross deformation. Investigation of these relationships leads to the development of a new principle of virtual work and a form of energy called stress energy. The concept of stress energy has been developed by considering the potential energy of the forces applied to the structure or mechanism and its relationship to Libove's from of complementary energy and Charlton's virtual work method has been discussed.

Smart control of cylindrical shells incorporating Murakami Zig-Zag function

The present work fills a gap on the postbuckling behavior of multilayer functionally graded graphene platelet reinforced composite (FG-GPLRC) cylindrical and spherical shell panels resting on elastic foundations subjected to central pinching forces and pressure loadings. Based on a higher-order shear deformation theory and the von Karman’s nonlinear strain–displacement relations, the governing equations of the FG-GPLRC cylindrical and spherical shell panels are established by the principle of virtual work. The non-uniform rational B-spline (NURBS) based isogeometric analysis (IGA), the modified arc-length method and the Newton’s iteration method are employed synthetically to obtain nonlinear load–deflection curves for the panels numerically. Several comparative examples are performed to test reliability and accuracy of IGA and arc-length method in present formulation and programming implementation. Parametric investigations are carried out to illustrate the effects of dispersion type of the graphene platelet (GPL), weight fraction of the GPL, thickness of the panel, radius of the panel and parameters of elastic foundation on the load–deflection curves of the FG-GPLRC shell panels. Some complex load–deflection curves of the FG-GPLRC cylindrical and spherical shell panels resting on elastic foundations may be useful for future references.

Instead of using the previous straight beam element to approximate the curved beam, in this paper, a curvilinear coordinate is employed to describe the deformations, and a new curved beam element is proposed to model the curved beam. Based on exact nonlinear strain-displacement relation, virtual work principle is used to derive dynamic equations for a rotating curved beam, with the effects of axial extensibility, shear deformation and rotary inertia taken into account. The constant matrices are solved numerically utilizing the Gauss quadrature integration method. Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system. The present results are compared with those obtained by commercial programs to validate the present finite method. In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation, comparison of the results of the present formulation with those of the ADAMS software are made. Furthermore, the present results obtained from linear formulation are compared with those from nonlinear formulation, and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.

Large deformations of cord-reinforced multilayered shells

Geometric nonlinear formulation for curved beams with varying curvature

TO undertake a successful computation task w.r.t. the construction and operation process of engineering structures, one of the mostly concerned obstacles is the limited or incomplete capability to automatically generate regular grid or to re-mesh retorted grid for complex structure domain containing structural planes and undergoing finite deformation. This chapter presents the principle and basic algorithm of the “element free Galerkin method (EFGM)” in structural dynamics that belongs to the family of “mesh-free methods (MFMs)”. In EFGM, the basis functions no longer belong to standard PU (e.g. the shape functions of fundamental FEM), instead, they are created from the neighborhood field nodes in an “influence or support domain” of any shape by the technique of “moving least squares (MLS)” approximation. The nodal variables in the piecewise trial function may be solved from the algebraic equation set according to the virtual work principle or variational principle (weak form). In this manner, no rigorous restraint is imposed on the generation of scattered field nodes (points), which allows for a great simplification in the pre-process work of complex engineering structure. Although it has not outperformed FEMs in the routine problems of geotechnical and hydraulic structures, yet EFGM exhibits great expectation due to its flexibility in handling structural planes, crack growth, and other large deformation issues.

A new curved quadrilateral composite shell element using vectorial rotational variables is presented. An advanced co‐rotational framework defined by the two vectors generated by the four corner nodes is employed to extract pure element deformation from large displacement/rotation problems, and thus an element‐independent formulation is obtained. The present line of formulation differs from other co‐rotational formulations in that (i) all nodal variables are additive in an incremental solution procedure, (ii) the resulting element tangent stiffness is symmetric, and (iii) is updated using the total values of the nodal variables, making solving dynamic problems highly efficient. To overcome locking problems, uniformly reduced integration is used to compute the internal force vector and the element tangent stiffness matrix. A stabilized assumed strain procedure is employed to avoid spurious zero‐energy modes. Several examples involving composite plates and shells with large displacements and large rotations are presented to testify to the reliability, computational efficiency, and accuracy of the present formulation. Copyright © 2011 John Wiley & Sons, Ltd.

A finite element procedure is presented for the analysis of rubber-like hyperelastic materials. The volumetric incompressibility condition of rubber deformation is included in the formulation using the penalty method, while the principle of virtual work is used to derive a nonlinear finite element equation for the large displacement problem that is presented in a total-Lagrangian description. The behavior of rubber deformation is represented by hyperelastic constitutive relations based on a generalized Mooney-Rivlin model. The proposed finite element procedure using analytic differentiation exhibited results that matched very well with those from the well-known commercial packages NISA II and ABAQUS. Furthermore, the convergence of equilibrium iteration is quite slow or frequently fails in the case of near-incompressible rubber. To prevent such phenomenon even for the case that Poisson's ratio is very close to 0.5, Poisson's ratio of 0.49000 is used, first, to get an approximate solution without any difficulty; then the applied load is maintained and Poisson's ratio is increased to 0.49999 following a proposed pattern and adopting a technique of relaxation by monitoring the convergence rate. For a given Poisson ratio near 0.5, with this approach, we could reduce the number of substeps considerably.

Thermo-mechanical analysis of porous sandwich S-FGM plate for different boundary conditions using Galerkin Vlasov's method: A semi-analytical approach