A computer graphics program for measuring two- and three-dimensional form change in developing craniofacial cartilages using finite element methods

Allometric analysis of chondrocranial growth seeks to provide objective measures of morphogenetic form change during ontogeny of the primordial skull. Linear measures, typically employed to study differential growth, become problematic at the histological level since an external referencing system is impossible to achieve for microscopic anatomies in embryos. The purpose of this paper is to describe a computer graphics program which generates spatially invariant measures of two- and three-dimensional form change using finite element methods. Anatomical form change is viewed as a continuous deformation of an initial finite element representing an anatomical unit into a second configuration. The algorithm consists of isoparametric scaling of finite elements, strain matrix formulation, and size/shape variable derivation. The routine includes four segments serving to extract nodal data, generate the strain matrix relating the two morphologies as well as deriving corresponding size/shape variables, reference the major and minor axes of form change, and provide graphic display of the anatomical geometries. Applications are provided measuring two- and three-dimensional form change in the developing craniofacial cartilages of rats subjected to treatment with the known teratogen diazo-oxo-norleucine (DON). The finite element routine provides craniofacial form change variables which are expected in light of cellular alterations induced by DON administration. Finally, computational differences between this routine and similar approaches using finite element methods for analyzing biological form change are examined.     

A three-dimensional finite element program to predict ultimate fracture failure load

A finite element computer program using an eight-noded three-dimensional isoparametric finite element is developed to predict the initiation and propagation of fracture, load-displacement history and failure load in elastoplastic structural systems subjected to monotonically increasing loads. Isotropie material is considered. The program is based on small deformation theory and uses an incremental loading technique to load the structure. The approach uses two types of piecewise linear approximations for the non-linear portion of the actual uniaxial stress-strain curve for the material: (i) the tangent modulus concept and (ii) the secant modulus concept. Either the St. Venant or von Mises yielding criteria can be used to predict yielding or fracture. Three different methods of calculating element principal stresses/strains are incorporated to apply the yield criterion. The energy at fracture is redistributed by using the ‘zero modulus unload-reload scheme’. Two different problems are solved using the developed program to demonstrate its capabilities and accuracy: (i) a center cracked panel and (ii) a tubular T-connection. The results obtained by the finite element analyses compare well with the available results from experimental tests on similar specimens.     

A program for perspective views of three-dimensional surfaces

A numerical method is proposed for solving linear differential equations of second order without first derivatives. The new method is superior to de Vogelaere's for this class of equations, and for non-linear equations it becomes an implicit extension of de Vogelaere's method. The global truncation error at a fixed steplength h is bounded by a term of order h⁴, and the interval of absolute stability is [?2.4, 0]. The work of Coleman and Mohamed (1978) is readily adapted to provide truncation error estimates which can be used for automatic error control. It is suggested that the new method should be used in preference to de Vogelaere's for linear equations, and in particular to solve the radial Schrödinger equation. the radial Schrödinger equation.     

A desk-top personal computer for finite element post-processing

There is low cost, effective software for data processing available for use with desk-top personal computers. One such software package, called VisiCalc, is used on a TRS80 personal computer as a complement to some mainframe finite element post-processing. The TRS80 was attached to a time-sharing computer system to transfer some ADINA data to the TRS80's diskettes so that the data could then be reviewed with VisiCalc after disconnecting from the time-sharing system. VisiCalc post-processing was limited to review and graphical display of data that represented the contact pressure between a tire model and a road surface. However, the techniques and specialized programming can be easily extended to provide other types of data reduction and review. Also, the procedures are directly extendable to other desk-top personal computers.     

A finite element quasi-Eulerian method for three-dimensional fluid-structure interactions

A quasi-Eulerian approach is used in the development of a three-dimensional hydrodynamic finite element. With this approach the motion of the computing grid may be different from the motion of the material. Within each element the field variables are represented by trilinear interpolation functions and the pressure field is assumed to be constant. This leads to a set of simple relations for internal nodal forces that are easily coded and computationally efficient. Because the formulation is based upon a rate approach it is applicable to problems involving large displacements. The technique of degeneration is applied to the hexahedron to generate a pentahedral element. The use of the hour-glass dissipating nodal-forces for mesh stabilization is discussed. The procedure used to couple the fluid and structural domains of a problem is presented. The above method is applied to a three-dimensional, fluid-structure interaction problem in the area of reactor safety.     

A simple contour plotting program for finite element output

An algorithm to produce piecewise linear contour plots for finite element output is described. Several examples are shown to demonstrate the application of the algorithm.     

A computer program for kinematic analysis of three-dimensional cascaded linkage chains

The KIN program analyses the motion of three-dimensional cascaded linkage chains consisting of combinations of four-bar linkage units, axial translation units, and sliders (units confined to motion along a fixed line). Motion can be simulated for any combination of geometrical parameters. The model, the program, input-output features and an application are described. The program is written in PL/1, and can be run in either batch or conversational mode.     

A mixed interface finite element for cohesive zone models

The phenomena of crack initiation, propagation and ultimate fracture are studied here under the following assumptions: (i) the crack law is modelled by means of a cohesive zone model and (ii) the crack paths are postulated a priori. In this context, a variational formulation is proposed which relies on an augmented Lagrangian. A mixed interface finite element is introduced to discretise the crack paths, the degrees of freedom of which consist in the displacement on both crack lips and the density of cohesive forces. This enables an exact treatment of multi-valued cohesive laws (e.g. initial adhesion, contact conditions, possible rigid unloading, etc.), without penalty regularisation.A special attention is paid to the convergence with mesh-refinement, i.e. the well-posedness of the problem, on the basis of theoretical results of contact mechanics and some complementary numerical investigations. Fulfilment of the LBB condition is the key factor to gain the desired properties. Moreover, it is shown that the integration of the constitutive law admits a unique solution as soon as some condition on the augmented Lagrangian is enforced. Finally, a 3D simulation shows the applicability to practical engineer problems, including in particular the robustness of the formulation and its compatibility with classical solution algorithms (Newton method, line-search, path-following techniques).     

Attribute specification for finite element models

Two different approaches for the application of problem specific attributes to finite element models are discussed. In both approaches interactive computer graphics techniques and the use of a top-down program approach is emphasized. The major difference in the approaches is the point during problem definition that the attributes are applied and manifests itself primarily in the program's database with little effect on program operation. Program operation is demonstrated through the use of an example problem. Finally, the advantages and disadvantages of the two approaches are discussed.     

A computer algebra based finite element development environment

A finite element development environment based on the technical computing program Mathematica is described. The environment is used to automatically program standard element formulations and develop new elements with novel features. Source code can also be exported in a format compatible with commercial finite element program user-element facilities. The development environment is demonstrated for three mixed Petrov–Galerkin plane stress elements: a standard formulation, an advanced formulation incorporating rotational degrees of freedom and a standard formulation in which the stiffness matrix is integrated analytically, before being exported as ANSYS user elements. The results presented illustrate the accuracy of the standard mixed formulation element and the enhancement of performance when rotational degrees of freedom are added. Further, the analytically integrated element shows that computational requirements can be greatly reduced when analytical integration schemes are used in the formation.     

A simple algorithm for three-dimensional finite element analysis of contact problems

This paper addresses the numerical solution of three-dimensional frictionless contact problems by a finite element method. The two-body contact problem is considered in the context of fully non-linear kinematics. The impenetrability constraint is satisfied via a classical penalty formulation. The contacting surfaces are discretized by means of projections of the interacting element faces onto suitably chosen flat surfaces. Attention is focused on the efficiency of the overall algorithm. Numerical simulations are conducted for a series of test problems to assess the performance of the proposed methodology.     

A general isoparametric finite element program SDRC SUPERB

SDRC SUPERB is a general purpose finite element program that performs linear static, dynamic and steady state heat conduction analyses of structures made of isotropic and/or orthotropic elastic materials having temperature dependent properties. The finite element library of SUPERB contains isoparametric plane stress, plane strain, flat plate, curved shell, solid type curved shell and solid elements in addition to conventional beam and spring elements. Linear, quadratic and cubic interpolation functions are available for all isoparametric elements. Independent parameters such as displacements and temperatures are obtained from SUPERB using the stiffness method of analysis. The remaining dependent parameters, such as stresses and strains, are evaluated at element gauss points and extrapolated to nodal locations. Averaged values are given as final output. The graphic capabilities of SUPERB consists of geometry and distorted geometry plotting, and stress, strain and temperature contouring. Contours are plotted at user defined cutting planes for solids and at top, middle or bottom surfaces for plate and shell types of structures.In the first part of this paper, the program capabilities of SUPERB are summarized. Extrapolation techniques used for determining dependent nodal parameters and for contour plotting are explained in the second part of the paper. Behavior of standard, wedge and transition type isoparametric elements and the effect of interpolation function orders on accuracy are discussed in the third part. The results of several illustrative problems are included.     

A three-dimensional state space finite element solution for laminated composite cylindrical shells

On the basis of the theory of three-dimensional elasticity, this paper presents a state space finite element solution for stress analysis of cross-ply laminated composite shells. This is a continuation of the authors’ previously published work on laminated plates [Compos. Struct. 57 (1–4) (2002) 117; Comput. Methods Appl. Mech. Engrg. 191 (37–38) (2002) 4259]. Once again a state space formulation is introduced to solve for through-thickness stress distributions, while the traditional finite elements are used to approximate the in-surface variations of state variables. A three-dimensional laminated shell element is established in an arbitrary orthogonal curvilinear coordinate system, while the application of the element is shown by calculating stresses in laminated cylindrical shells. Compared with the traditional finite element method, the new solution provides accurate continuous through-thickness distributions of both displacements and transverse stresses.     

A general three-dimensional L-section beam finite element for elastoplastic large deformation analysis

In this paper, the development of a general three-dimensional L-section beam finite element for elastoplastic large deformation analysis is presented. We propose the generalized interpolation scheme for the isoparametric formulation of three-dimensional beam finite elements and the numerical procedure is developed for elastoplastic large deformation analysis. The formulation is general and effective for other thin-walled section beam finite elements. To show the validity of the formulation proposed, a 2-node three-dimensional L-section beam finite element is implemented in an analysis code. As numerical examples, we first perform elastic small and large deformation analyses of a cantilever beam structure subjected to various tip loadings, and elastoplastic large deformation analysis of the same structure under reversed cyclic tip loading. We then analyze the failures of simply supported beam structures of different lengths and slenderness ratios under elastoplastic large deformation. The same problems are solved using refined shell finite element models of the structures. The numerical results of the L-section beam finite element developed here are compared with the solutions obtained using shell finite element analyses. We also discuss the numerical solutions in detail.     

Local refinement of three-dimensional finite element meshes

Mesh refinement is an important tool for editing finite element meshes in order to increase the accuracy of the solution. Refinement is performed in an iterative procedure in which a solution is found, error estimates are calculated, and elements in regions of high error are refined. This process is repeated until the desired accuracy is obtained.Much research has been done on mesh refinement. Research has been focused on two-dimensional meshes and three-dimensional tetrahedral meshes ([1] Ning et al. (1993) Finite Elements in Analysis and Design, 13, 299–318; [2] Rivara, M. (1991) Journal of Computational and Applied Mathematics 36, 79–89; [3] Kallinderis; Vijayar (1993) AIAA Journal,31, 8, 1440–1447; [4] Finite Element Meshes in Analysis and Design,20, 47–70). Some research has been done on three-dimensional hexahedral meshes ([5] Schneiders; Debye (1995) Proceedings IMA Workshop on Modelling, Mesh Generation and Adaptive Numerical Methods for Partial Differential Equations). However, little if any research has been conducted on a refinement algorithm that is general enough to be used with a mesh composed of any three-dimensional element (hexahedra, wedges, pyramids, and/or retrahedra) or any combination of three-dimensional elements (for example, a mesh composed of part hexahedra and part wedges). This paper presents an algorithm for refinement of three-dimensional finite element meshes that is general enough to refine a mesh composed of any combination of the standard three-dimensional element types.