Abstract

Many finite elements exhibit the so‐called ‘volumetric locking’ in the analysis of incompressible or quasi‐incompressible problems.In this paper, a new approach is taken to overcome this undesirable effect. The starting point is a new setting of the governing differential equations using a finite calculus (FIC) formulation. The basis of the FIC method is the satisfaction of the standard equations for balance of momentum (equilibrium of forces) and mass conservation in a domain of finite size and retaining higher order terms in the Taylor expansions used to express the different terms of the differential equations over the balance domain. The modified differential equations contain additional terms which introduce the necessary stability in the equations to overcome the volumetric locking problem. The FIC approach has been successfully used for deriving stabilized finite element and meshless methods for a wide range of advective–diffusive and fluid flow problems. The same ideas are applied in this paper to derive a stabilized formulation for static and dynamic finite element analysis of incompressible solids using linear triangles and tetrahedra. Examples of application of the new stabilized formulation to linear static problems as well as to the semi‐implicit and explicit 2D and 3D non‐linear transient dynamic analysis of an impact problem and a bulk forming process are presented.

Abstract

Based on the classical laminated plate theory, a variational approach for the study of the statical and dynamical behaviour of arbitrary quadrilateral anisotropic plates with various boundary conditions is developed. The analytical formulation uses the Ritz method in conjunction with natural coordinates to express the geometry of general plates in a simple form. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated using the Gram–Schmidt procedure. The algorithm developed is quite general and can be used to study fibre reinforced composite laminates with symmetric lay-ups, which may have general anisotropy and any combinations of clamped, simply supported and free edge support conditions. Various numerical applications are presented and some results are compared with existing values in the literature to demonstrate the accuracy and flexibility of the present method. New results were also determined for plates with different geometrical shapes, combinations of boundary conditions, several stacking sequences and various angles of fibre orientation.

Abstract

The paper presents a new triangle for analysis of laminate plates and shells. The in-plane degrees of freedom are interpolated quadratically whereas a linear layer-wise approximation is chosen for the normal displacement. A substructuring technique is used to eliminate the in-plane degrees of freedom during the assembly process thus reducing substantially the computationed costs. The element performance is evaluated in the static and dynamic analysis of di€erent laminate plate and shell structures

Abstract

Abstract

Abstract

The present work aims to carry out comparative analyzes (dynamic and static) in generic cross-sections with variable inertias in parabolic corbels. For this, a computational program was developed in the language FORTRAN 90/95 via the Finite Element Method, and its results were compared with those found in the literature. Therefore, through the displacement, acceleration and velocity data found in the analyses, it was possible to verify the influence of dynamic loading on the structural behavior of beams and frames. The damping of the structure, called proportional damping or Rayleigh damping, was taken into account, including the properties of the materials used, which in this research were steel and wood. The analyzed element has generic cross-sections with the inertia varying in parabolic corbel along its length, so that they can be used in increasingly innovative architectural projects. Finally, the formulation corresponding to the Three-Dimensional Finite Element was implemented, which allows the static analysis of the structure with the hexahedral finite element with eight nodes (H₈), hexahedral finite element with twenty nodes (H₂₀).

Abstract

The present work aims to carry out comparative analyzes (dynamic and static) in generic cross-sections with variable inertias in parabolic corbels. For this, a computational program was developed in the language FORTRAN 90/95 via the Finite Element Method, and its results were compared with those found in the literature. Therefore, through the displacement, acceleration and velocity data found in the analyses, it was possible to verify the influence of dynamic loading on the structural behavior of beams and frames. The damping of the structure, called proportional damping or Rayleigh damping, was taken into account, including the properties of the materials used, which in this research were steel and wood. The analyzed element has generic cross-sections with the inertia varying in parabolic corbel along its length, so that they can be used in increasingly innovative architectural projects.
Finally, the formulation corresponding to the Three-Dimensional Finite Element was implemented, which allows the static analysis of the structure with the hexahedral finite element with eight nodes (H8), hexahedral finite element with twenty nodes (H20).