Search results

A previously presented finite element shell formulation is extended to the application of large strains. The finite elements are those based on the concept of ‘the degenerated solids’, which are widely used in non‐linear finite element programs. The constitutive equation of hyperelastic incompressible material is adopted and specialized to the Mooney‐Rivlin law. The additional state variable, the hydrostatic pressure, which occurs for incompressible materials, is eliminated on element level using the plane stress condition. Attention is drawn to the efficient calculation of the element matrices by applying a layer concept. The effectiveness of the proposed total Lagrangian formulation is demonstrated in a number of example problems.

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.

This paper deals with structural shape and thickness optimization of axisymmetric shell structures loaded symmetrically. In the finite element stress analysis use is made of newly developed linear, quadratic, and cubic, variable thickness, C(0) elements based on axisymmetric Mindlin‐Reissner shell theory. An integrated approach is used to carry out the whole shape optimization process in a fully automatic manner. A robust, versatile and flexible mesh generator is incorporated with facilities for generating either uniform or graded meshes, with constant, linear, or cubic variation of thickness, pressure etc. The midsurface geometry and thickness variations of the axisymmetric shell structure are defined using cubic splines passing through certain key points. The design variables are chosen as the coordinates and/or the thickness at the key points. Variable linking procedures are also included. Sensitivity analysis is carried out using either a semi‐analytical method or a global finite difference method. The objective of the optimization is the weight minimization of the structure. Several examples are presented illustrating optimal shapes and thickness distributions for various shells. The changes in the bending, membrane and shear strain energies during the optimization process are also monitored.

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.

The paper aims to present a method of implementing layered shell finite elements for punching shear analysis of reinforced concrete slabs. The emphasis is on the influence of different material modelling parameters on the calculated results.

The finite element approach utilizes quadratic isoparametric C⁰ shell elements. The elements take into account an out‐of‐plane shear response and allow implementation of three‐dimensional constitutive models and out‐of‐plane reinforcement. Through the consideration of 3D states of strain and stress, the formulation can predict structural failures caused by either flexure or punching shear.

Comparisons are shown between analytical solutions and several test results, which show that the presented non‐linear finite element formulation works well for modelling slab behaviour.

The most important contribution of this work is the use of shell elements for punching and flexure analysis of reinforced concrete slabs and the discussion on the influence of material modelling on the calculated results. Shell finite elements have been extensively used in the analysis of slabs for flexure. However, the critical issue in the design of these slabs is a 3D shear effect around the column area called punching shear. 3D elements can be used for punching shear analysis of reinforced concrete slabs, but the cost of using these elements and the computational effort make them impractical for real design situations. Therefore, shell finite elements, with appropriate element and material modelling formulations that make them applicable for punching shear analysis, are employed in the presented work.

Presents a robust and unconditionally stable return‐mapping algorithm based on the discrete counterpart of the principle of maximum plastic dissipation. Develops the explicit expression for the consistent elasto‐plastic tangent modulus. All expressions are derived via tensor formulation showing the advantage over the classical matrix notation. The integration algorithm is implemented in the formulation of the four‐node isoparametric assumed‐strain finite‐rotation shell element employing the Mindlin‐Reissner‐type shell model. By applying the layered model, plastic zones can be displayed through the shell thickness. Material non‐linearity described by the von Mises yield criterion and isotropic hardening is combined with a geometrically non‐linear response assuming finite rotations. Numerical examples illustrate the efficiency of the present formulation in conjunction with the standard Newton iteration approach, in which no line search procedures are required. Demonstrates the excellent performance of the algorithm for large time respective load steps.

A new four‐node (non‐flat) general quadrilateral shell element for geometric and material non‐linear analysis is presented. The element is formulated using three‐dimensional continuum mechanics theory and it is applicable to the analysis of thin and thick shells. The formulation of the element and the solutions to various test and demonstrative example problems are presented and discussed.

The purpose of this paper is to present an accurate and efficient element for analysis of spherical shell structures.

A scaled boundary finite element method is proposed, which offers more advantages than the finite element method and boundary element method. Only the boundary of the computational domain needs to be discretized, but no fundamental solution is required.

The method applies to thin as well as thick spherical shells, irrespective of the shell geometry, boundary conditions and applied loading. The numerical solution converges to highly accurate result with raising the order of high-order elements.

The modeling strictly follows three-dimensional theory of elasticity. Formulation of the surface finite elements using three translational degree of freedoms per node is required, which results in considerably simplifying the computation. In the thickness directions, it is solved analytically, no problem of high aspect ratio arises and transverse shear locking can be successfully avoided.

A simple triangular shell element which incorporates the effects of coupling between membrane and flexural behaviour and avoids membrane locking is described. The element uses a discrete Kirchhoff bending formulation and a constant strain membrane element. For the purpose of permitting inextensional modes and thus avoiding membrane locking, a decomposition technique, which can also be viewed as a strain projection method, is used. The method is illustrated first for a beam element and then for a triangular shell element. Results are presented for a variety of linear static problems to illustrate its accuracy and some highly non‐linear problems to indicate its applicability to collapse analysis.

This paper aims to develop a simple and efficient shell element for large strains hyper‐elastic analyses.

Based on the classical MITC4 shell element formulation a 3D shell element with finite strain kinematics is developed. The new quadrilateral shell element has five dof per node and two global dof to model the thickness stretching. The shell element is implemented for hyperelastic material models and the application of different hyperelastic constitutive relations is discussed.

The results obtained considering three of the hyperelastic material models available in the literature are quite different when the developed strains are relatively high; this indicates that, for analyzing actual engineering examples, experimental data should be used to decide on the most suitable constitutive relation.

The 3D version of the MITC4 element was developed.