Search results

In this work we present interrelations between different finite rotation parametrizations for geometrically exact classical shell models (i.e. models without drilling rotation). In these kind of models the finite rotations are unrestricted in size but constrained in the 3‐d space. In the finite element approximation we use interpolation that restricts the treatment of rotations to the finite element nodes. Mutual relationships between different parametrizations are very clearly established and presented by informative commutative diagrams. The pluses and minuses of different parametrizations are discussed and the finite rotation terms arising in the linearization are given in their explicit forms.

In this paper we derive a simple finite element formulation for geometrical nonlinear shell structures. The formulation bases on a direct introduction of the isoparametric finite element formulation into the shell equations. The element allows the occurrence of finite rotations which are described by two independent angles. A layerwise linear elastic material model for composites has been chosen. A consistent linearization of all equations has been derived for the application of a pure Newton method in the nonlinear solution process. Thus a quadratic convergence behaviour can be achieved in the vicinity of the solution point. Examples show the applicability and effectivity of the developed element.

A simple beam element is developed for the solution of large deflection problems. The total Lagrangian formulation is based on the kinematic relations proposed by Reissner for finite rotations and stretching as well as shearing of plane beams. The motion is discretized by linear expansions of the global displacement components and the cross‐sectional rotation in two‐dimensional Euclidean space yielding a simple beam element with three degrees of freedom at the two nodes. The shear locking is reduced by selective integration in order to eliminate the spurious shear constraint similar to interdependent variable interpolation. The large rotation formulation is compared with two forms of moderate rotation theories which have been used in the past to develop the geometric stiffness properties for linear stability analysis of the so‐called Mindlin plate elements. The predictive value of different geometric stiffness approximations is assessed with several examples which range from the static and kinetic stability analysis of the classical Euler‐column to the large deflection problem of a clamped beam.

Implementation details of the assumed shear strain method in a novel finite rotation shell theory are discussed. Careful considerations of the pertinent aspects of the Newton solution procedure are given. The latter results in a very robust performance of the presented 4–node shell element in some challenging finite rotation problems.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

Aims to address the issues pertaining to dynamics of constrained finite rotations as a follow‐up from previous considerations in statics.

A conceptual approach is taken.

In this work the corresponding version of the Newmark time‐stepping schemes for the dynamics of smooth shells employing constrained finite rotations is developed. Different possibilities to choose the constrained rotation parameters are discussed, with the special attention given to the preferred choice of the incremental rotation vector.

The pertinent details of consistent linearization, rotation updates and illustrative numerical simulations are supplied.

This paper aims to describe the formulation of a displacement-based triangular membrane finite element with true drilling rotational degree of freedom (DOF).

The presented formulation incorporates the true drilling rotation provided by continuum mechanics into the displacement field by way of using the polynomial interpolation. Unlike the linked interpolation, that uses a geometric transformation between displacement and vertex rotations, in this work, the interpolation of the displacement field in terms of nodal drilling rotations is obtained following an unusual approach that does not imply any presumed geometric transformation.

New relationship linking the mid-side normal displacement to corner node drilling rotations is derived. The resulting new element with true drilling rotation is compatible and does not include any problem-dependent parameter that may influence the results. The spurious zero-energy mode is stabilized in a careful way that preserves the true drilling rotational degrees of freedom (DOFs).

Several works dealing with membrane elements with vertex rotational DOFs have been published with improved convergence rate, however, owing to the need for incorporating rotations in the finite element meshes involving solids, shells and beam elements, having finite elements with true drilling rotational DOFs is more appreciated.

Addresses the computational aspects involved in the numerical simulation of sheet stamping processes. Focuses on some numerical aspects of the intrinsic complexity of these problems, the first of which is the necessity to take into account properly membrane and bending effects. Presents a well‐adapted shell element. The second aspect concerns the description and the implementation of the initial orthotropic plastic behaviour for sheet metal parts, based on a formulation in a rotating frame using the initial microstructure rotation. The stress calculation algorithm is based on a particular implementation of the elastic predictor‐plastic corrector method. The last aspect concerns the solution procedures with a particular development concerning the treatment of the blankholder load as a constraint. A set of computational results validated with experiments prove the accuracy of the proposed approach in solving stamping problems.

In order to avoid the problem of volumetric locking often encountered when using constant strain tetrahedral finite elements, the purpose of this paper is to present a new composite tetrahedron element which is especially designed for the combined finite-discrete element method (FDEM).

A ten-noded composite tetrahedral (COMPTet) finite element, composed of eight four-noded low order tetrahedrons, has been implemented based on Munjiza’s multiplicative decomposition approach. This approach naturally decomposes deformation into translation, rotation, plastic stretches, elastic stretches, volumetric stretches, shear stretches, etc. The problem of volumetric locking is avoided via a selective integration approach that allows for different constitutive components to be evaluated at different integration points.

A number of validation cases considering different loading and boundary conditions and different materials for the proposed element are presented. A practical application of the use of the COMPTet finite element is presented by quantitative comparison of numerical model results against simple theoretical estimates and results from acrylic fracturing experiments. All of these examples clearly show the capability of the composite element in eliminating volumetric locking.

For this tetrahedral element, the combination of “composite” and “low order sub-element” properties are good choices for FDEM dynamic fracture propagation simulations: in order to eliminate the volumetric locking, only the information from the sub-elements of the composite element are needed which is especially convenient for cases where re-meshing is necessary, and the low order sub-elements will enable robust contact interaction algorithms, which maintains both relatively high computational efficiency and accuracy.

A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given. The bibliography at the end of the paper contains 1,726 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1996‐1999.