Finite element bending analysis of nonuniform circular plates

The finite element method is applied to the small deflection bending analysis of nonuniform thin axisymmetric circular plates made of linear elastic material. Elements with annular and circular geometry with only 4 degrees of freedom are used in the analysis of both symetrically and nonsymmetrically loaded plates. Non-symmetric loads are expanded in Fourier series and elements restricted to deform with specified number of nodal diameters are used for each component of loading. The method is checked with several numerical examples. Although applicable to only axisymmetric plates, the method gives better results compared to other finite element methods besides offering savings in computer storage and time.     

Nonlinear vibration of cord-reinforced composite shells

This paper discusses ADINA finite element incremental formulations for nonlinear static and dynamic analysis of materials with nonlinear constitutive equations. The formulations are applied to axisymmetric problems of cord reinforced composites using the ADINA computer program. Numerical results on natural frequencies and mode shapes of cord reinforced inflatable toroidal shells are presented for axisymmetric modes of excitation.     

The usefulness of static condensation in the finite element analysis of stiffened submersible cylindrical hulls

The usefulness of the static condensation technique in the finite element analysis of stiffened submersible. cylindrical hulls is examined in this paper. The finite element formulation used herein is essentially the same as outlined by the authors in an earlier paper wherein the stiffener is modeled rigorously using axisymmetric thin annular plate elements for the web and axisymmetric thin shell elements for the flange. The static condensation technique has been applied in this paper to reduce these stiffener finite elements so that their effect can be transferred to the shell node at the point of attachment of the stiffener with the shell. The advantage of such condensation of the stiffener elements is the smaller number of equations to be solved without the rigor of the stiffener modeling being lost in any way. The manner of incorporating the condensation in the computer program has been described. Examples of several stiffened submersible cylindrical hulls have been considered as an illustration of the use of the program.     

Elastic-plastic-fracture analysis of concrete structures

The paper presents a computer implementation technique for an elastic-plastic-fracture analysis of concrete structures. To this end, the finite element formulation for a fractured concrete element as well as the relevant redistribution procedure of released stresses are described. Further, it is discussed how the finite element method may be applied effectively in the analysis of concrete structures subjected to different types of loading conditions. In particular, in order to avoid the structure-load system interaction during an unstable process of material fracturing, two extreme loading conditions are considered: (1) dead load, and (2) the load applied by a rigid testing machine. This leads in turn to a pure load and a pure displacement-control analysis. Based on the computer program developed, two typical computational examples are presented involving nonlinear progressive collapse analysis of split-cylinder test, and implosion analysis of a concrete cylindrical hull.     

Dynamic finite element analysis of nonaxisymmetric structures

A dynamic finite element method of analysis is developed for structural configurations which are derived from axisymmetric geometries but contain definite nonaxisymmetric features in the circumferential direction. The purpose of the analysis is to develop a method which will take into consideration the fact that the stress and strain conditions in these geometries will be related to the corresponding axisymmetrie solution. This analysis is an extension of previously published work in which a similar approach was developed for static structural problems. The analysis is developed in terms of a cylindrical coordinate system r, θ and z. As the first step of the analysis, the geometry is divided into several segments in the r-θ plane. Each segment is then divided into a set of quadrilateral elements in the r-z plane. The axisymmetric displacements are obtained for each segment by solving a related axisymmetric configuration. A perturbation analysis is then performed to match the solutions at certain points between the segments, and obtain the perturbation displacements for the total structure. The total displacement is then the axisymmetric displacement plus the perturbation displacement. The analysis allows for elastic-plastic materials with orthotropic yield criterion based on Hill's yield function and kinematic strain hardening. The finite element dynamic equations are solved by finite differences by dividing the time domain into incremental steps. The solution has been programmed on a computer and applied to a number of examples.     

Interactive-adaptive geometrically nonlinear analysis of shell structures

This paper presents an investigation of interactive-adaptive techniques for nonlinear finite element structural analysis. In particular, effective methods leading to reliable automated, finite element solutions of nonlinear shell problems are of primary interest here. This includes automated adaptive nonlinear solution procedures based on error estimation and adaptive step length control, reliable finite elements that account for finite deformations and finite rotations, three-dimensional finite element modeling, and an easy-to-use, easy-to-learn graphical user interface with three-dimensional graphics. A computational environment, which interactively couples a comprehensive geometric modeler, an automatic three-dimensional mesh generator and an advanced nonlinear finite element analysis program with real-time computer graphics and animation tools, is presented. Three examples illustrate the merit and potential of the approaches adopted here and confirm the feasibility of developing fully automated computer aided engineering environments.     

Complementary error bounds for foolproof finite element mesh generation

The use of complementary variational principles in finite element analysis is examined. It is shown that complementary finite element solutions provide an element by element measure of the accuracy of the solution. By solving a problem repeatedly, beginning with a coarse mesh and refining those elements having the largest errors, an automatic, foolproof finite element mesh generation procedure is developed. Finite element solutions obtained by the new procedure have the property that the finest elements are concentrated in regions of greatest need while large elements are found in less important regions. A computer program which implements the new algorithm is described and examples of finite element solutions generated by the program are presented.     

A computer program for perspective projection of three-dimensional finite element models

The theoretical basis of a computer program prepared for plotting the perspectives of 3-D finite element models with consideration of the hidden line removal technique is presented. The algorithm is successfully implemented in a FORTRAN 77 program. The validity of the algorithm and its implementation is verified through use of two typical examples. The program may be used in input data error correction and output data reduction of finite element programs.     

Optimum design of structures composed of metal and composite materials

This paper describes a general program system in the optimum design of structures. The element library in the program system consists of a bar (BAR), a shear trapezoidal panel (STP), a constant strain triangle (CST), a plate linear isoparametric element (PLIE), and a beam element in a plane (BEAM). The structural design procedure is performed by combining finite element analysis and hybrid approximation technique with dual solutions. It is suitable for structures with various materials (metal, composite, etc.), especially the structures of the aircraft (wing, tail, fuselage, etc.). Five examples show that the computer program system is capable of generalized applicability.     

Finite element methods for the solution of some incompressible non-newtonian fluid mechanics problems with free surfaces

A finite element scheme suitable for incompressible fluid flow in plane and axisymmetric geometries is constructed by using a Galerkin method. Principal features of the associated computer program are that it can be used for problems with or without free surfaces, with or without inertia, and for many types of non-Newtonian flow. Here we describe the use of the program in solving Poiseuille flow, a 2:1 contraction tube flow, free non-Newtonian jets without inertia, and a Newtonian free jet problem at a Reynolds number of 10. Comparison with exact solutions, other computer solutions and experiment is given where such information is available.     

Thermal stress analysis of reentry vehicle nosetips at angle of attack

The ASAAS (Asymmetric Stress Analysis of Axisymmetric Solids) computer program is applied to the prediction of thermal stresses in a reentry vehicle nosetip subjected to asymmetric temperature distributions and angle-of-attack loadings during reentry. This three-dimensional stress analysis computer program has the unique capability of properly accounting for the circumferential variation of temperature dependent material properties. It is based on a meridional finite element discretization of an axisymmetric solid combined with a Fourier series representation of circumferentially dependent variables. In contrast with similar methods where material properties cannot be expressed as a function of temperature, this method requires that the large system of equations be solved simultaneously. This is handled efficiently in ASAAS by several newly developed approaches to stiffness matrix generation and simultaneous equation solution.

The nosetip analyzed is fabricated from an orthotropic, temperature dependent graphite material that is susceptible to thermal shock. Analyses are performed at several points in a trajectory and the effects of both aerodynamic heating and pressure loading are considered. The complete states of temperature, stress, strain and displacement throughout the graphite material are obtained as a product of ASAAS. Results are presented in the form of meridional contour plots at selected circumferential stations.

The usefulness of ASAAS in performing angle-of-attack analysis of nosetips is evaluated by comparison to an axisymmetric analysis based on single ray heating. In addition, the convergence of solutions with increasing numbers of harmonics is demonstrated and computer run times are discussed.     

An edge-based data structure for two-dimensional finite element analysis

The introduction of engineering work stations has made it possible for an analyst to describe a two-dimensional finite element model and view its response in a real-time, interactive graphical environment. This interactive environment puts severe performance restrictions on finite element programs. The programs must be able to respond to an analyst's request in a reasonable amount of time. The traditional finite element data structures cannot provide the required performance. This paper introduces a new application of an existing data structure, the winged-edge, which can provide the required performance. The winged-edge data structure is described, with particular emphasis given to its use for finite element analysis. The implementation of the data structure in a fracture analysis program is discussed and a number of examples of its use are presented.     

A 4 CST quadrilateral element for incompressible materials and nearly incompressible materials

We introduce a quadrilateral element for plane strain or axisymmetric analysis of incompressible or nearly incompressible materials. This quadrilateral is made of four constant strain triangles. The divergence is taken as constant over the quadrilaterals; Lagrange multipliers are avoided by using a penalty function approach. Numerical examples are given. Such an element can also be used for the solution of Navier-Stokes equations.     

Axisymmetric element analysis using analytical computing

In axisymmetric finite element analysis numerical instability occur when the elements are located too far from the symmetry axis. By a complete analytical analysis this problem is explained, and it is shown to be more severely with quadratic displacement fields than with the linear ones.The basic element analysis is very lengthy and possible only with the aid of the FORMAC analytical computer language. However, the final results for stiffness matrix and consistent load and mass matrices are relatively simple and suitable for programming.     

A low cost interactive graphics system for large scale finite element analyses

The development of an interactive graphics system for use with finite element programs in a production analysis environment is described. This new system is believed to offer considerable cost savings, both in terms of initial expenditures and running costs compared with other systems, while simultaneously offering greatly expanded capacity and diversity of graphics options.

Other advantages include: ease of personnel training, the ability to operate on any reasonably sized computer, improved picture quality and resolution, and a high degree of program independence. The system, which is fully operational at Lockheed Missiles and Space Company's Missile System Division, is described in detail together with examples of available options. Finally, Lockheed's experience with the system is described and future developments discussed.     

Rapid reanalysis by the force method

A procedure to reanalyze a damaged structure using a finite element force method of analysis is presented. Unlike similar methods that use the displacement method of analysis, the procedure presented here yields a direct, rather than an iterative method. A computer program was written and illustrative examples were solved and are presented herein. Residual elastic strength is defined and calculated for damaged structures that were originally optimally designed for minimum weight.     

Elasto-plastic analysis of axisymmetric structures subject to arbitrary loads by hybrid-stress finite elements

A semi-analytic finite element method in conjuction with a hybrid-stress functional based on the initial stress approach is presented for elasto-plastic analysis. A three-dimensional solid element based on hybrid-stress model is also implemented for the elasto-plastic analysis. A procedure to compute the non-linear effects in terms of Fourier series in the hybrid-stress model is described. The accuracy and efficiency of the semi-analytic method is evaluated via numerical examples by comparing the solution with a full 3-D solution. The semi-analytic method is observed to be a viable alternative to 3-D analysis in elasto-plastic analysis of axisymmetric structures subject to arbitrary loads.     

A parallel finite element method and its prototype implementation on a hypercube

This paper describes a parallel implementation of the finite element method on a multiprocessor computer. The proposed strategy does not require the formation of global system equations. An element or substructure is mapped onto each processor of the multiple-instruction, multiple-data multiprocessing system. Throughout the program, each processor stores only the information relevant to its element (substructure) and generates the local stiffness matrix. A parallel element (substructure) oriented conjugate gradient procedure is employed to compute the displacements. Each processor then determines the strains and stresses for its associated element (substructure). A prototype implementation of this parallel finite element program strategy on a hypercube computer is discussed. Examples for both linear and nonlinear analyses are presented.     

A unified approach for the analysis of bridges,plates and axisymmetric shells using the linear mindlin strip element

In this paper a finite strip formulation which allows to treat bridges, axisymmetric shells or plate structures of constant transverse cross section in an easily and unified manner is presented. The formulation is based on Mindlin's shell plate theory. One dimensional finite elements are used to discretize the transverse section and Fourier expansions are used to define the longitudinal/circumferential behavior of the structure. The element used is the simple two noded strip element with just one single integrating point. This allows to obtain all the element matrices in an explicit and economical form. Numerical examples for a variety of straight and curve bridges, axisymmetric shells and plate structures which show the efficiency of the formulation and accuracy of the linear strip element are given.