Evaluation of a finite-element analysis for longitudinal vibrations of liquid propellant launch vehicles
Evaluation of finite element analysis for longitudinal vibrations of liquid propellant launch vehicle
Pinson, L. D.↗
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Results for “finite-element analysis”
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Rapid iterative reanalysis for automated design
A method for iterative reanalysis in automated structural design is presented for a finite-element analysis using the direct stiffness approach. A basic feature of the method is that the generalized stiffness and inertia matrices are expressed as functions of structural design parameters, and these generalized matrices are expanded in Taylor series about the initial design. Only the linear terms are retained in the expansions. The method is approximate because it uses static condensation, modal reduction, and the linear Taylor series expansions. The exact linear representation of the expansions of the generalized matrices is also described and a basis for the present method is established. Results of applications of the present method to the recalculation of the natural frequencies of two simple platelike structural models are presented and compared with results obtained by using a commonly applied analysis procedure used as a reference. In general, the results are in good agreement. A comparison of the computer times required for the use of the present method and the reference method indicated that the present method required substantially less time for reanalysis. Although the results presented are for relatively small-order problems, the present method will become more efficient relative to the reference method as the problem size increases. An extension of the present method to static reanalysis is described, ana a basis for unifying the static and dynamic reanalysis procedures is presented.
Bhatia, K. G.↗
Improved hardening theory for cyclic plasticity.
A temperature-dependent version of a combined hardening theory, including isotropic and kinematic hardening, is presented within the framework of recent plasticity formulations. This theory has been found to be especially useful in finite-element analysis of aerospace vehicle engines under conditions of large plastic strain and low-cycle fatigue.
Vos, R. G.↗
Plasticity - Theory and finite element applications.
A unified presentation is given of the development and distinctions associated with various incremental solution procedures used to solve the equations governing the nonlinear behavior of structures, and this is discussed within the framework of the finite-element method. Although the primary emphasis here is on material nonlinearities, consideration is also given to geometric nonlinearities acting separately or in combination with nonlinear material behavior. The methods discussed here are applicable to a broad spectrum of structures, ranging from simple beams to general three-dimensional bodies. The finite-element analysis methods for material nonlinearity are general in the sense that any of the available plasticity theories can be incorporated to treat strain hardening or ideally plastic behavior.
Armen, H., Jr.↗
Two-dimensional finite-element temperature variance analysis
The finite element method is extended to thermal analysis by forming a variance analysis of temperature results so that the sensitivity of predicted temperatures to uncertainties in input variables is determined. The temperature fields within a finite number of elements are described in terms of the temperatures of vertices and the variational principle is used to minimize the integral equation describing thermal potential energy. A computer calculation yields the desired solution matrix of predicted temperatures and provides information about initial thermal parameters and their associated errors. Sample calculations show that all predicted temperatures are most effected by temperature values along fixed boundaries; more accurate specifications of these temperatures reduce errors in thermal calculations.
Heuser, J. S.↗
Finite Element Method for Thermal Analysis
A two- and three-dimensional, finite-element thermal-analysis program which handles conduction with internal heat generation, convection, radiation, specified flux, and specified temperature boundary conditions is presented. Elements used in the program are the triangle and tetrahedron for two- and three-dimensional analysis, respectively. The theory used in the program is developed, and several sample problems demonstrating the capability and reliability of the program are presented. A guide to using the program, description of the input cards, and program listing are included.
Heuser, J.↗
A finite-element method for the plastic buckling analysis of plates
Finite element technique extended for plastic buckling of flat plates, using Stowell theory
Isakson, G.↗
Nonlinear behavior of shells of revolution under cyclic loading
A large deflection elastic-plastic analysis is presented, applicable to orthotropic axisymmetric plates and shells of revolution subjected to monotonic and cyclic loading conditions. The analysis is based on the finite-element method. It employs a new higher order, fully compatible, doubly curved orthotropic shell-of-revolution element using cubic Hermitian expansions for both meridional and normal displacements. Both perfectly plastic and strain hardening behavior are considered. Strain hardening is incorporated through use of the Prager-Ziegler kinematic hardening theory, which predicts an ideal Bauschinger effect. Numerous sample problems involving monotonic and cyclic loading conditions are analyzed. The monotonic results are compared with other theoretical solutions.
Levine, H. S.↗
Nonlinear behavior of shells of revolution under cyclic loading.
A large deflection elastic-plastic analysis is presented applicable to orthotropic axisymmetric plates and shells of revolution subjected to monotonic and cyclic loading conditions. The analysis is based on the finite-element method. It employs a new higher order, fully compatible, doubly curved orthotropic shell-of-revolution element using cubic Hermitian expansions for both meridional and normal displacements. Both perfectly plastic and strain hardening behavior are considered. Strain hardening is incorporated through use of the Prager-Ziegler kinematic hardening theory, which predicts an ideal Bauschinger effect. Numerous sample problems involving monotonic and cyclic loading conditions are analyzed.
Levine, H. S.↗
Finite element analysis of compressible solids with nonlinear material properties
Finite-element computer program solves for nodal point displacements in an axisymmetric solid. The options in the program include plane stress analysis, axisymmetric solids analysis, nonlinear /plastic/ analysis, and equivalent stress and strain.
Wilson, E. L.↗
Automatic data generation scheme for finite-element method /FEDGE/ - Computer program
Algorithm provides for automatic input data preparation for the analysis of continuous domains in the fields of structural analysis, heat transfer, and fluid mechanics. The computer program utilizes the natural coordinate systems concept and the finite element method for data generation.
Akyuz, F.↗
NASTRAN thermal analyzer: A general purpose finite element heat transfer computer program
The program not only can render temperature distributions in solids subjected to various thermal boundary conditions, including effects of diffuse-gray thermal radiation, but is fully compatible in capacity and in the finite-element model representation with that of its structural counterpart in the NASTRAN system. The development history of the finite-element approach for determining temperatures is summarized. The scope of analysis capability, program structure, features, and limitations are given with the objective of providing NASTRAN users with an overall veiw of the NASTRAN thermal analyzer.
Lee, H.↗
Finite element analysis of large transient elastic-plastic deformations of simple structures, with application to the engine rotor fragment containment/deflection problem
Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.
Wu, R. W.↗
Recent advances in numerical analysis of structural eigenvalue problems
A wide range of eigenvalue problems encountered in practical structural engineering analyses is defined, in which the structures are assumed to be discretized by any suitable technique such as the finite-element method. A review of the usual numerical procedures for the solution of such eigenvalue problems is presented and is followed by an extensive account of recently developed eigenproblem solution procedures. Particular emphasis is placed on the new numerical algorithms and associated computer programs based on the Sturm sequence method. Eigenvalue algorithms developed for efficient solution of natural frequency and buckling problems of structures are presented, as well as some eigenvalue procedures formulated in connection with the solution of quadratic matrix equations associated with free vibration analysis of structures. A new algorithm is described for natural frequency analysis of damped structural systems.
Gupta, K. K.↗
Analysis of the dynamics of thin primary mirrors for large astronomical telescopes
The NASTRAN structural analysis program was used to investigate the dynamic properties of thin primary mirrors suitable for use in large orbiting astronomical telescopes. An analysis is included of the mode shapes and modal frequencies for several thin, homogeneous, isotropic mirrors. Typical cases include two different mirror diameters, two different diameter-to-thickness ratios, and both a mirror without and a mirror with a central hole that is 22 percent of the mirror diameter. The finite-element structural model is evaluated by comparing the NASTRAN generated results with theoretical values for a simply supported, flat, circular mirror. The same model is then used for evaluating the spherical mirrors. The mode shapes and frequencies of a 0.762-meter-diameter mirror with a 60-to-1 diameter-to-thickness ratio and a three-point rigid kinematic (not overconstrained) mount are calculated and plotted for comparison with results obtained previously from the SAMIS structural analysis program for this same mirror. A static analysis is also shown for comparison with experimentally obtained influence coefficients.
Ostroff, A. J.↗
Dynamic response analysis of geometrically non-linear structures subjected to high impact.
Description of an efficient digital computer method for the determination of the propagation of elastic stresses and deformations in certain geometrically nonlinear structures subjected to high impact loading. The finite-element matrix displacement approach utilizing curved quadrilateral shell elements in conjunction with a nodewise predictor-corrector method employing Runge-Kutta extrapolation techniques has been adopted for the present solution. The related computer program written in FORTRAN V for the UNIVAC 1108 computer has proved to be effective for the solution of a range of practical problems including rectangular and cylindrical panels. Numerical results are presented for a relevant structure, the cell container, and the negative electrode of an impact-resistant battery subjected to high impact, simulating its free landing on a planetary surface.
Gupta, K. K.↗
Mathematical modeling of spinning elastic bodies for modal analysis.
The problem of modal analysis of an elastic appendage on a rotating base is examined to establish the relative advantages of various mathematical models of elastic structures and to extract general inferences concerning the magnitude and character of the influence of spin on the natural frequencies and mode shapes of rotating structures. In realization of the first objective, it is concluded that except for a small class of very special cases the elastic continuum model is devoid of useful results, while for constant nominal spin rate the distributed-mass finite-element model is quite generally tractable, since in the latter case the governing equations are always linear, constant-coefficient, ordinary differential equations. Although with both of these alternatives the details of the formulation generally obscure the essence of the problem and permit very little engineering insight to be gained without extensive computation, this difficulty is not encountered when dealing with simple concentrated mass models.
Likins, P. W.↗
Assessment of advances in structural analysis for space shuttle
The latest technology for structural analysis in relation to the design tasks that lie ahead for the space shuttle is reviewed. For shell-of-revolution structures, the analysis can be formulated as a one-dimensional problem which is readily solved by using finite-difference or numerical-integration techniques. For more general asymmetric shells, a two-dimensional formulation is required. However, the governing equations are readily formulated and are amenable to solution by finite-difference techniques. For a completely general structural arrangement, such as structural frameworks, recourse is usually made to discretized formulations using finite elements. Of course, the finite-element programs could be used for shell structures, but at a loss in accuracy and increase in computer time compared with the special purpose programs.
Dixon, S. C.↗