Eight-node Hexahedral Finite Element Research Articles

3D Structural Topology Optimization Using ESO, SESO and SERA: Comparison and an Extension to Flexible Mechanisms

This article investigates the study of Topology Optimization (TO) in 3D elasticity problems to determine the optimal topology by applying the evolutionary methods of Smoothing Evolutionary Structural Optimization (SESO), Sequential Element Rejection and Admission (SERA), and Evolutionary Structural Optimization (ESO). These procedures were implemented in MATLAB code as an extension of Top3d implemented for SIMP by using the eight-node hexahedral finite element formulation in three-dimensional elastostatic structures. The approaches conducted in the present study are demonstrated with numerical examples involving the compliance minimization criterion. Further, a brief synthesis of flexible mechanisms was studied to emphasize the performance of complaint mechanisms measured in terms of two design specifications/functionalities: mechanical and geometrical advantages, which are the highlights of this article. To show the gains of the proposed methods, numerical results obtained are compared with Solid Isotropic Material with Penalization (SIMP) models.

A specific eight-node hexahedral finite element for the analysis of 3D fibre-reinforced composites

This contribution deals with the development of an eight-node hexahedral finite element to estimate the effective elastic properties of fibre-reinforced composite materials and structures. This three-dimensional (3D) composite element is a combination of the standard eight-node hexahedral element, modelling a unit of the matrix domain, and 3D two-node truss elements that represent fibres crossing each matrix element. The so-called ‘Projected Fibre Approach’ is then considered to express the truss elements variables in terms of their corresponding matrix elements. Consequently, the obtained system of equations size is equivalent to that of a non-reinforced medium. In particular, we show that the proposed finite element formulation allows readily studying 3D composite structures with complex shape of the reinforcement like stitched sandwich panels.

A fluid-structure interaction model for numerical simulation of bridge flutter using sectional models with active control devices. Preliminary results

A fluid-structure interaction scheme for numerical simulation of actively controlled bridges subject to flutter instability is proposed in this work. In order to suppress or attenuate dynamic instabilities induced by the wind action on long-span bridges, control systems are proposed considering aerodynamic appendices and winglets attached to the deck structure, where control forces are continuously calculated using optimal control theory. The flow fundamental equations are solved here employing the explicit two-step Taylor-Galerkin method and the arbitrary Lagrangian-Eulerian (ALE) description. Eight-node hexahedral finite elements with one-point quadrature and hourglass stabilization are utilized for spatial discretization. Flow turbulence is modeled using Large Eddy Simulation (LES) and a partitioned coupling scheme is adopted for fluid-structure interactions. The structural system is analyzed considering the sectional model approach and a rigid-body formulation for large rotations. Different control techniques and winglet configurations are investigated using prismatic and bridge cross-sections, where control efficiency is evaluated in terms of displacement reduction and energy required by the control system. Preliminary results are obtained here employing approximate flow conditions to verify the control algorithm, where laminar flows and a two-dimensional LES-type approach are utilized.

An Eight-Node Hexahedral Finite Element with Rotational DOFs for Elastoplastic Applications

Abstract In this paper, the earlier formulation of the eight-node hexahedral SFR8 element is extended in order to analyze material nonlinearities. This element stems from the so-called Space Fiber Rotation (SFR) concept which considers virtual rotations of a nodal fiber within the element that enhances the displacement vector approximation. The resulting mathematical model of the proposed SFR8 element and the classical associative plasticity model are implemented into a Fortran calculation code to account for small strain elastoplastic problems. The performance of this element is assessed by means of a set of nonlinear benchmark problems in which the development of the plastic zone has been investigated. The accuracy of the obtained results is principally evaluated with some reference solutions.

Geometric non-linear hexahedral elements with rotational DOFs

This paper presents an extension of two recently published conforming and non conforming eight-node hexahedral finite elements, presenting rotational degrees of freedom in addition to the classical displacement ones, to analyze geometric nonlinear problems. Their formulations are based on the so-called space fiber rotation concept that considers virtual rotations of a nodal fiber within the element which enhances the displacement vector approximation. To demonstrate the efficiency and accuracy of the proposed finite elements, several beam and shell nonlinear assessment tests are presented and the obtained results are principally compared with the classical first-order and second-order hexahedral elements responses as well as other advanced elements from the literature. In particular, it is shown that the proposed elements allow a correct prediction of the studied structures nonlinear behaviors including snap-through and snap-back instabilities and the accuracy of the non conforming element is close to the classical 20-node hexahedral element.

A multilayered 3D hexahedral finite element with rotational DOFs

The study presents a multilayer eight-node hexahedral finite element with rotational degree of freedom to model composite laminate structures. Its formulation is based on virtual rotations of a nodal fibre within the element that enriches the displacement vector approximation. A particular attention is made to the determination of transverse deflections as well as in-plane stresses. To assess the accuracy of the proposed element, several benchmarks are considered and the obtained results are compared with 3D elasticity solutions and other advanced finite elements from the literature.

An Efficient Model for Numerical Simulation of the Mechanical Behavior of Soils. Part 1: Theory and Numerical Algorithm

A numerical model to simulate the mechanical behavior of soils is presented in this first part of the present work. This paper reports some advances obtained in the first stage of an ongoing research, which aims to develop a robust and efficient algorithm for consolidation analyses of saturated/unsaturated soils. Hence, the present work is mainly concerned with basic issues, such as efficiency of the finite element formulation and accuracy of the constitutive formulation. Since geotechnical materials exhibit elastoplastic characteristics, the theory of plasticity is applied here by means of the critical state concept using the Cam-Clay formulation. The constitutive equation is integrated using an explicit algorithm where the strain increment is divided into a number of sub-steps defined automatically by the numerical scheme. Eight-node hexahedral finite elements with one-point quadrature are employed in the spatial discretization of the geometrical domain. In order to avoid excitation of spurious modes, an efficient hourglass control is utilized in conjunction with a corotational formulation, which also contributes to the treatment of geometrical and physical nonlinearities.

A solid-shell layerwise finite element for non-linear geometric and material analysis

The application of layerwise theories to correctly model the displacement field of sandwich structures or laminates with high modulus ratios usually employs plate or facet-shell finite element formulations to compute the element stiffness and mass matrices for each layer. In this work an alternative approach is proposed, using a high performance hexahedral finite element to represent the individual layer mass and stiffness. This eight-node hexahedral finite element is formulated based on the application of the enhanced assumed strain method (EAS) to solve several locking pathologies coming from the high aspect ratio of the finite element and the usual incompressibility condition of the core materials. The solid-shell finite element formulation is introduced in the layerwise theory through the definition of a projection operator, based on the finite element variables transformation matrix. The non-linear geometric and material capabilities are introduced into the finite element formulation, allowing for the representation of large displacements, large deformation and material non-linear behaviors. The developed formulation is numerically tested and benchmarked, being validated by using published experimental results obtained from sandwich specimens.

On the implementation of the EAS and ANS concept into a reduced integration continuum shell element and applications to sheet forming

This contribution deals with the application of a new solid-shell finite element based on reduced integration with hourglass stabilization in the field of sheet metal forming. The formulation includes the enhanced assumed strain (EAS) concept getting by with a minimum of enhanced degrees-of-freedom to overcome the volumetric locking and Pois- son’s thickness locking. To circumvent further the well-known effects of curvature thickness locking and transverse shear locking present in standard eight-node hexahedral finite elements the assumed natural strain (ANS) concept is applied. The implementation of the latter key feature is not straight-forward in reduced integration solid-shells. The second crucial point is a combined Taylor expansion of the compatible Green-Lagrange strain tensor with respect to the center of the element and the normal through the element center leading to an efficient and locking-free hourglass stabilization. Due to the three-dimensional modeling of the structure fully three-dimensional materials can be implemented without additional assumptions. Furthermore simulations of double-side contact problems (e.g. sheet metal forming) benefit from an exact modeling of the sheet thickness.

Geometric nonlinear dynamic analysis of plates and shells using eight-node hexahedral finite elements with reduced integration

This work presents a geometric nonlinear dynamic analysis of plates and shells using eight-node hexahedral isoparametric elements. The main features of the present formulation are: (a) the element matrices are obtained using reduced integrations with hourglass control; (b) an explicit Taylor-Galerkin scheme is used to carry out the dynamic analysis, solving the corresponding equations of motion in terms of velocity components; (c) the Truesdell stress rate tensor is used; (d) the vector processor facilities existing in modern supercomputers were used. The results obtained are comparable with previous solutions in terms of accuracy and computational performance.

Numerical errors and uncertainties in finite-element modeling of trabecular bone

Although micromechanical finite-element models are being increasingly used to help interpret the results of bio-mechanical tests, there has not yet been a systematic study of the numerical errors and uncertainties that occur with these methods. In this work, finite-element models of human L1 vertebra have been used to analyze the sensitivity of the calculated elastic moduli to resolution, boundary conditions, and variations in the Poisson’s ratio of the tissue material. Our results indicate that discretization of the bone architecture, inherent in the tomography process, leads to an underestimate in the calculated elastic moduli of about 20% at 20 μm resolution; these errors vary roughly linearly with the size of the image voxels. However, it turns out that there is a cancellation of errors between the softening introduced by the discretization of the bone architecture and the excess bending resistance of eight-node hexahedral finite elements. Our empirical finding is that eight-node cubic elements of the same size as the image voxels lead to the most accurate calculation for a given number of elements, with errors of less than 5% at 20 μm resolution. Comparisons with mechanical testing are also hindered by uncertainties in the grip conditions; our results show that these uncertainties are of comparable magnitude to the systematic differences in mechanical testing methods. Both discretization errors and uncertainties in grip conditions have a smaller effect on relative moduli, used when comparing between different specimens or different load directions, than on an absolute modulus. The effects of variations in the Poisson’s ratio of the bone tissue were found to be negligible

A multiple-quadrature eight-node hexahedral finite element for large deformation elastoplastic analysis

A multiple-quadrature underintegrated hexahedral finite element, which is free of volumetric and shear locking, and has no spurious singular modes, is described and implemented for nonlinear analysis. Finite element formulations are derived in the corotational coordinate system. The use of consistent tangent operators for large deformation elastoplasticity with nonlinear isotropic/kinematic hardening rules preserves the quadratic rate of convergence of the Newton's iteration method in static analysis. Test problems studied demonstrate the efficiency and effectiveness of this element in solving a wide variety of problems, including sheet metal forming processes.