An enriched finite element model for heat transfer simulation of checkerboard structures with singular behaviour

In this paper, we propose an automatic procedure to improve the accuracy of finite element solutions using enriched 2D solid finite elements (4-node quadrilateral and 3-node triangular elements). The enriched elements can improve solution accuracy without mesh refinement by adding cover functions to the displacement interpolation of the standard elements. The enrichment scheme is more effective when used adaptively for areas with insufficient accuracy rather than the entire model. For given meshes, an error for each node is estimated, and then proper degrees of cover functions are applied to the selected nodes. A new error estimation method and cover function selection scheme are devised for the proposed adaptive enrichment scheme. Herein, we demonstrate the proposed enrichment scheme through several 2D problems.

Unified analysis of enriched finite elements for modeling cohesive cracks

An enriched finite element for simulation of groundwater flow to a well or drain

A new enriched finite element for fatigue crack growth

A three-dimensional enriched finite element method for nonlinear transient heat transfer in functionally graded materials

Use of an enriched shell finite element to simulate delamination-migration in a composite laminate

PurposeThe purpose of this paper is to present the extension of plane wave based method.Design/methodology/approachThe mixed functional are discretized using enriched finite elements. The fluid is discretized by enriched acoustic element, the structure by enriched structural finite element and the interface fluid‐structure by fluid‐structure interaction element.FindingsResults obtained show the potentialities of the proposed method to solve a much larger class of wave problems in mid‐ and high‐frequency ranges.Originality/valueThe plane wave based method has previously been applied successfully to finite element and boundary element models for the Helmholtz equation and elastodynamic problems. This paper describes the extension of this method to the vibro‐acoustic problem.

Intensity of singularity in three-material joints under shear loading: Two-real singularities and power-logarithmic singularities

Crack problems in a viscoelastic medium using enriched finite element method

The simplicial vector linear finite elements are commonly employed for the numerical solution of the stationary Stokes equations. Nevertheless, they exhibit significant limitations when applied to more complex scenarios. In response to these shortcomings, Bernardi and Raugel introduced an enriched finite element which is a generalization of the conventional simplicial vector linear finite element. It employs polynomials as enrichment functions and its application extends across a broad spectrum of practical engineering computational fields. However, for some types of problems, these enrichment functions are not very efficient. The main goal of this paper is to introduce a comprehensive method for enhancing the simplicial vector linear finite element with non-polynomial enrichment functions. The enriched finite element is defined concerning any simplex and can be considered an extension of the Bernardi and Raugel finite element. A crucial component in this context is the characterization result, formulated regarding the nonvanishing of a specific determinant. This result provides both necessary and sufficient conditions for the existence of families of enriched elements. In conclusion, we present numerical tests that show the efficacy of the suggested enrichment strategy.

A new enriched 4-node 2D solid finite element free from the linear dependence problem

Low-order elements are widely used and preferred for finite element analysis, specifically the three-node triangular and four-node tetrahedral elements, both based on linear polynomials in barycentric coordinates. They are known, however, to under-perform when nearly incompressible materials are involved. The problem may be circumvented by the use of higher degree polynomial elements, but their application become both more complex an computationally expensive. For this reason, non-polynomial enriched finite element methods have been proposed for solving engineering problems. In line with previous researches, the main contribution of this paper is to present a general strategy for enriching the standard simplicial linear finite element by non-polynomial functions. A key role is played by a characterization result, given in terms of the non-vanishing of a certain determinant, which provides necessary and sufficient conditions, on the enrichment functions and functionals, that guarantee the existence of families of such enriched elements. We show that the enriched basis functions admit a closed form representation in terms of enrichment functions and functionals. Finally, we provide concrete examples of admissible enrichment functions and perform some numerical tests.

Enriched finite element methods for Timoshenko beam free vibration analysis

Many important interface crack problems are inherently three-dimensional in nature, e.g., debonding of laminated structures at corners and holes. In an effort to accurately analyze three-dimensional interface fracture problems, an efficient computational technique was developed that utilizes enriched crack tip elements containing the correct interface crack tip asymptotic behavior. In the enriched element formulation, the stress intensity factors K I, K II, and K III are treated as additional degrees of freedom and are obtained directly during the finite element solution phase. In this study, the results that should be of greatest interest are obtained for semi-circular surface and quarter-circular corner cracks. Solutions are generated for uniform remote tension and uniform thermal loading, over a wide range of bimaterial combinations. Of particular interest are the free surface effects, and the influence of Dundurs’ material parameters on the strain energy release rate magnitudes and corresponding phase angles.

New enriched finite elements with softening plastic hinges for the modeling of localized failure in beams