Isoparametric Hexahedral Elements Research Articles

A hexahedral face element for elastoacoustic vibration problems

A finite-element method to compute elastoacoustic vibration modes in 3D problems is analyzed. It is based on displacement formulations for solid and fluid. The discretization consists of classical isoparametric hexahedral elements for the former and hexahedral Raviart–Thomas elements for the latter, to avoid spurious modes. The meshes on fluid and solid domains do not need to coincide on the common interface, since the kinematic constraint is weakly imposed. The generalized eigenvalue problem is written in a matrix form which allows using a standard MATLAB eigensolver. Numerical results showing the good performance of the method and the convenience of using incompatible meshes are reported.

Optimal impact resistance design for RC slabs

In this study, an attempt was made to develop a useful design support system for RC slabs by combining a 3-D nonlinear dynamic FEM newly developed in our laboratory for impact failure behavior and an immune algorithm (IA) with which multiple quasi-optimum solutions can be obtained. For the analysis of impact failure behavior, layered nonlinear FEM models with thin plate bending elements, and three-dimensional elastoplastic FEM models with 8-node isoparametric hexahedral elements were used. First, an existing IA was modified to make it suitable for RC slab designing, and both genetic and immune algorithms were applied to optimization problems with multiple optimum solutions, as well as quasi-optimization problems with multiple maximum values. By comparing the above two approaches, the usefulness of the IA for design problems with discrete parameters was verified. Next, indices for evaluating impact resistance were discussed, and design simulation was conducted based on the indices by combining the layered nonlinear FEM and the IA. From the results obtained, the precision and usefulness of the IA-based design support system are discussed. For obtaining a more practical design support system, shear reinforcement was taken into account by combining the IA with the three- dimensional elastoplastic FEM. Furthermore, the effectiveness and future potential of the design support system were confirmed by investigating the effect of introducing a database of design plans.

Study of a 3-D FEM combined with the slab method for shape rolling

A complex model which combines the rigid–plastic 3-D FEM with the slab method is developed in this paper. In this model, first the plastic deformation zone in the billet was divided into several slabs, each slab being divided into 40 eight-node hexahedral isoparametric elements. Then, the rigid–plastic theory was combined with the equilibrium condition of the slab method. Finally, the metal flow, roll pressure, strain and strain ratio, etc. were calculated. Compared with the rigid–plastic 3-D FEM, this complex model confirmed the result to be within an acceptable error. Not only could a great deal of simulation time and storage capacity of CPU be saved, but it was also very suitable in performance for personal computers.

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.

Modeling Compression Failure after Low Velocity Impact on Laminated Composites Using Interface Elements

Low velocity impact damage can significantly reduce the residual strength of laminated composites. This kind of damage (mostly delaminations) is very dangerous for the structures because it is not apparent to the naked eye and, in some cases, it can reduce the compressive residual strength up to 60%. In this work, a numerical model for predicting the compression failure of laminated composites containing delamination caused by low velocity impact was developed. An interface finite element, previously developed by the authors, was used. This element is compatible with twenty-seven node isoparametric hexahedral elements and enables modeling the behavior of the damaged interface, taking into account a three-dimensional stress state, the interpenetration constraint and the propagation of delamination. In order to verify the numerical model, some experimental work was done. The experimental work, performed on carbon-epoxy (04, 904)5 and (904, 04), laminates, included low velocity impact tests using a drop weight testing machine, followed by X-Ray damage characterization and compression tests using a fixture system similar to IITRI system. The numerical and experimental results were compared and good agreement was obtained.

Three-dimensional modeling of magnetotelluric data using finite element method

The magnetotelluric response of a resistivity model is usually obtained by solving a boundary value problem of the Helmholtz type equation which follows from the Maxwell's equation. In this case, the electric field is not continuous at the boundary between different resistivity media. This condition gives us to errors in the numerical modelling using the finite element method or the finite difference method. To overcome this, I formulated the finite element equation using secondary field components resulting from the anomalies. The primary field is calculated analytically for a semi-infinite uniform or horizontally layered earth. I use the finite element method composed of 8 nodes isoparametric hexahedral elements to calculate the secondary field excited by electric charges appears at the anomalies having different resistivity from the host medium. Current sources at the resistivity anomaly depend on the resistivity contrast and the primary electric field, which appears on the right hand side of the finite element equations. I use boundary conditions which take account of the asymptotic behavior of the secondary field far away from the resistivity boundary. I applied this modelling method to simple three-dimensional prism models and compared the results with the responses of the hybrid FEM (Gupta et al., 1987) and the integral equation modeling (Ting and Hohmann, 1981).

Analysis of current densities induced inside a human model by the two‐step process method combining the surface‐charge integral equation and the finite‐element method

AbstractTo analyze the density of the current induced in the human body by the coupling phenomena of the ac electric field and the human body, the integral‐equation method and the finite‐element method have been proposed. However, there is no effective method for the analysis of the induced current density including the directional component in the model with a three‐dimensional human body shape by taking into account the conductivity of human tissues.The authors have developed a method for the analysis of the induced current density in the three‐dimensional shape model by a two‐step process consisting of: (1) the derivation of the induced current flowing in from the surface of the human model by the surface charge method; and (2) the application of these values as the boundary values of the finite‐element method using an isoparametric hexahedral element. The model can analyze the induced current density in the model by directly considering the conductivity and the permittivity of the human tissues. The results of the analysis of the induced current density in the present model have been confirmed from the experimental results of the metallic human model with the identical shape.

Mesh generation and numerical simulation of fluid entering a large tube bundle

A three-dimensio nal finite element model is used to calculate fluid entering a tank containing a large array of tubes (assemblies). The time-dependent primitive equations of fluid motion are solved using equal order, isoparametric hexahedral elements. Petrov-Galerkin weighting, mass lumping, and reduced integration are utilized with explicit time marching. The tank is 7.5 m tall by 6.7 m in diameter, and contains a total of 600 tubes, consisting primarily of 10.8-cm-diam assemblies with some 2.5-cm-diam control rods. The 10.8-cm assemblies are hollow and thin shelled; the 2.5-cm control rods are solid. The fluid first flows into a plenum, then begins to drain into the assemblies, which are positioned below the plenum; the fluid subsequently discharges from the ends of the assemblies near the bottom of the tank and recirculates within the tank prior to returning to the plenum. A total of 623,040 elements was used to discretize the plenum and tank vessel. Over 30 MW of storage were required to execute the problem on a Cray Y-MP, necessitating the use of a special Cray sparse matrix solver. The numerical results predict a marked decrease in the amount of fluid available to the interior tubes.

The inverse mapping and distortion measures for 8-node hexahedral isoparametric elements

The inverse relations of the isoparametric mapping for the 8-node hexahedra are derived by using the theory of geodesics in differential geometry. Such inverse relations assume the form of infinite power series in the element geodesic coordinates, which are shown to be the skew Cartesian coordinates determined by the Jacobian of the mapping evaluated at the origin. By expressing the geodesic coordinates in turn in terms of the isoparametric coordinates, the coefficients in the resulted polynomials are suggested to be the distortion parameters of the element. These distortion parameters can be used to sompletely describe the inverse relations and the determinant of the Jacobian of the mapping. The meanings of them can also be explained geometrically and mathematically. These methods of defining the distortion measures and deriving the inverse relations of the mapping are completely general, and can be applied to any other two-or three-dimensional isoparametric elements.

Finite element analysis of three-dimensional potential flow in the blade passage of a centrifugal turbomachine

A finite element simulation is presented for steady, three-dimensional, incompressible, potential flow in a centrifugal turbomachine. The numerical algorithm was based on the Galerkin's principle on the isoparametric hexahedral elements with periodic conditions on the inlet and outlet surfaces of the blade passage. Detailed velocity and pressure fields in a radial pump are examined, and its hydraulic performance is discussed. Results show that flow has strong vortical structures. The flow speed on the meridional surface is smaller near the pressure side than near the suction side. Strong pressure variation occurs at the turning region where flow changes from the axial to radial direction. The hydraulic efficiency of the pump increases with the increasing volume flow rate below the design point, above which it decreases with increasing volume flow rate.

Interactive specification of three-dimensional multiblock topologies

A scheme is described in this paper to deal with the topological and geometrical data which must be specified for macro-block based mesh generators. The topological and geometrical data is inputted interactively with the aid of graphical facilities, which reduces the burden on users of editing such large data files. The corresponding mesh generator uses macro-blocks as geometrical primitives described by isoparametric hexahedral elements, each of twenty nodes, and subdivides them into required meshes.

IMPROVEMENT OF THREE‐DIMENSIONAL HYBRID HEXAHEDRAL ELEMENTS BY USING ORTHOGONAL APPROACH

Based on the orthogonal approach for hybrid element methods, refined three‐dimensional isoparametric hybrid hexahedral elements have been developed. The behaviour of the proposed models are discussed in respect of coordinate invariance, spurious zero energy modes and the ability to pass the patch test. By adopting the orthogonality of strain energy, the element stiffness matrix can be decomposed into a series of stiffness matrices in which the implementational effectiveness can be improved. A number of examples is used to demonstrate the implementation efficiency, accuracy and distortion insensitivity of the proposed elements, and its capacity of handling nearly incompressible materials

Finite Element Simulation of Three-Dimensional Plastic Deformation in Shape Rolling. 3rd Report. Simulation of Non-Steady-State Deformation around Front and Rear Ends.

Non-steady-state three-dimensional deformation around the front and the rear ends in shape rolling with grooved rolls is simulated by the rigid-plastic finite element method using the isoparametric hexahedral elements with eight nodes. To simulate complex non-steady-state deformation in shape rolling, a non-steady-state scheme using a remeshing technique is proposed. The workpiece is remeshed at each step of deformation to locate nodal points at the boundary of the interface between the roll and the workpiece. The present method can calculate not only the non-steady state deformation around the front and the rear ends but also steady-state-deformation. As examples of non-steady state simulation, rolling processes of bars and beams with grooved rolls are chosen. The deforming shape and the distributions of stress and strain for the workpiece in non-steady and steady states are computed.

Three‐dimensional finite element contact algorithm for metal forming

AbstractThis work presents a three‐dimensional rigid plastic finite element formulation. The workpiece is discretized with eight node hexahedral isoparametric elements. Friction is included in the formulation by means of a shear stress depending on the relative velocity between the workpiece and the tool. Special attention is given to the contact problems, and a three‐dimensional contact algorithm based on a discretization of the tool surface with triangular elements is presented.Finally, some selected examples are solved, in order to show the capabilities of the formulation.

Finite element simulation of three-dimensional plastic deformation in shape rolling. 1st report. Fully three-dimensional simulation of steady-state deformation.

Three-dimensional steady-state deformation in shape rolling with grooved rolls is simulated by the rigid-plastic finite element method using the isoparametric hexahedral elements with eight nodes. To simulate complex steady-state deformation in shape rolling, a method featuring both the steady-state and the nonsteady-state schemes is proposed. For the three-dimensional element mesh, the boundary conditions of metal flow along the curved roll surface and of friction between the roll and the workpiece are dealt with at each node over the interface. Contact of the nodal points with the roll surface and detachment from the surface are judged at each step of calculation. As examples of three-dimensional simulation, rolling processes of bars and beams with grooved rolls are chosen. The deforming shape and the distributions of stress and strain in the workpiece are computed.

Three-dimensional finite element analysis of block compression

Based on rigid-viscoplastic formulation three-dimensional finite element analysis was performed for block compression. Discretization of the variational form of the equilibrium equation is made with 8-node hexahedral isoparametric elements. In the treatment of the traction prescribed boundary condition, velocity dependent friction was used. Simulations of compression of simple rectangular blocks were performed for two geometries under two friction conditions for each geometry. Comparison of some of the computed results with experiments showed excellent agreement. The technique was further extended to take into account the presence of a neutral zone, occurrence of folding and lifting, and applied to the analysis of compression of a wedge-shaped block between two flat parallel dies. Again, the computed results predict the actual characteristics of deformation accurately.

A three dimensional finite element dynamic response analysis of a vertebra with experimental verification

A detailed three-dimensional finite element model of a vertebra was formulated for a more complete understanding of the mechanics of vertebral column support. It accounts for many anatomical details of the bone and minimizes geometric idealizations. Isoparametric hexahedral elements were used along with thin plate and thin shell elements. The intervertebral disc and articular facets were represented by boundary elements which could simulate axial, shear and torsional behavior. A technique was developed to generate a finite element mesh and a general finite element code was used to perform the analysis. To validate the model, controlled static and dynamic loading experiments were carried out on excised human vertebral segments. The applied loads approximated whole body loading conditions and strain was monitored at selected locations on the cortical bone surface.

The significance of axial stresses and out-of-plane restraints on the design of rotors

The importance of axial stresses in rotors and the effect of out-of-plane restraints at the hub, on the in-plane stresses are investigated by using the finite element technique, with a hexahedral isoparametric element. The stresses in a non-dimensional form are compared with the plane stress solution. The probable mode of deformation of rotors of various axial thicknesses is given. The use of the above method in the analysis of an asymmetric rotor is also demonstrated.

A three-dimensional finite element analysis of a steam generator channel-head-complex—Comparison of theory and experiment

The purpose of this investigation is to compare three-dimensional stress and displacement distributions determined analytically and experimentally: the geometry chosen was a steam generator channel-head-complex. The analytical procedure employed a three-dimensional elastic finite element approach, using linear, quadratic, cubic and mixed isoparametric hexahedral elements. The experimental procedure employed frozen stress photo-elastic models. Three different types of loading: internal pressure, nozzle moment and nozzle thrust, were considered and calculated stresses and displacements at selected points were compared with results generated by a photoelastic analysis. 1 The comparison showed generally close agreement between these two sets of results.