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NASA NTRS1974

Finite-element analysis of vibration and flutter of cantilever anisotropic plates

The hybrid stress finite element method is used to study the effects of filament angle and orthotropicity parameter on the vibration and flutter characteristics of cantilevered anisotropic plates. The results indicate a generally strong lack of monotonic dependence on filament angle. Also, the natural frequency in certain cases involving the first few modes, can become relatively insensitive to both filament angle and orthotropicity parameter for a range of filament angle beyond 70 deg. Values of critical dynamic pressure are obtained by a modal approach, in which the mode shapes are obtained by the hybrid stress method. Convergence of the modal method is rather rapid for the configurations analyzed, and a comparison of the method with an exact solution for the case of an isotropic simply supported plate shows that use of six modes gives excellent agreement.

Rossettos, J. N.↗

NASA NTRS1975

Finite-element formulations for problems of large elastic-plastic deformation

An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is ideally suited to isotropically hardening Prandtl-Reuss materials. Further, the formulation is given in a manner which allows any conventional finite element program, for 'small strain' elastic-plastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. The paper closes with a unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures. Further, a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain, and the inadequacies of some of these are commented upon.

Mcmeeking, R. M.↗

NASA NTRS1976

Finite-element analysis of dynamic fracture

Applications of the finite element method to the two dimensional elastodynamics of cracked structures are presented. Stress intensity factors are computed for two problems involving stationary cracks. The first serves as a vehicle for discussing lumped-mass and consistent-mass characterizations of inertia. In the second problem, the behavior of a photoelastic dynamic tear test specimen is determined for the time prior to crack propagation. Some results of a finite element simulation of rapid crack propagation in an infinite body are discussed.

Aberson, J. A.↗

NASA NTRS1977

Three dimensional finite-element analysis of finite-thickness fracture specimens

The stress-intensity factors for most of the commonly used fracture specimens (center-crack tension, single and double edge-crack tension, and compact), those that have a through-the-thickness crack, were calculated using a three dimensional finite-element elastic stress analysis. Three-dimensional singularity elements were used around the crack front. The stress intensity factors along the crack front were evaluated by using a force method, developed herein, that requires no prior assumption of either plane stress or plane strain. The calculated stress-intensity factors from the present analysis were compared with those from the literature whenever possible and were generally found to be in good agreement. The stress-intensity factors at the midplane for all specimens analyzed were within 3 percent of the two dimensional plane strain values. The stress intensity factors at the specimen surfaces were considerably lower than at the midplanes. For the center-crack tension specimens with large thickness to crack-length ratios, the stress-intensity factor reached a maximum near the surface of the specimen. In all other specimens considered the maximum stress intensity occurred at the midplane.

Raju, I. S.↗

NASA NTRS1977

Simplified and refined structural modeling for economical flutter analysis and design

A coordinated use of two finite-element models of different levels of refinement is presented to reduce the computer cost of the repetitive flutter analysis commonly encountered in structural resizing to meet flutter requirements. One model, termed a refined model (RM), represents a high degree of detail needed for strength-sizing and flutter analysis of an airframe. The other model, called a simplified model (SM), has a relatively much smaller number of elements and degrees-of-freedom. A systematic method of deriving an SM from a given RM is described. The method consists of judgmental and numerical operations to make the stiffness and mass of the SM elements equivalent to the corresponding substructures of RM. The structural data are automatically transferred between the two models. The bulk of analysis is performed on the SM with periodical verifications carried out by analysis of the RM. In a numerical example of a supersonic cruise aircraft with an arrow wing, this approach permitted substantial savings in computer costs and acceleration of the job turn-around.

Ricketts, R. H.↗

NASA NTRS1978

Numerical computation of transonic flows by finite-element and finite-difference methods

Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.

Hafez, M. M.↗

NASA NTRS1985

Algorithms for Finite-Element Equations

Five direct and five iterative algorithms for finite element equations in linear equilibrium problems investigated for number of parallel computer architectures and their basic computation methods compared.

Salama, M. A.↗

NASA NTRS1984

Three-dimensional finite-element analysis of chevron-notched fracture specimens

Stress-intensity factors and load-line displacements were calculated for chevron-notched bar and rod fracture specimens using a three-dimensional finite-element analysis. Both specimens were subjected to simulated wedge loading (either uniform applied displacement or uniform applied load). The chevron-notch sides and crack front were assumed to be straight. Crack-length-to-specimen width ratios (a/w) ranged from 0.4 to 0.7. The width-to-thickness ratio (w/B) was 1.45 or 2. The bar specimens had a height-to-width ratio of 0.435 or 0.5. Finite-element models were composed of singularity elements around the crack front and 8-noded isoparametric elements elsewhere. The models had about 11,000 degrees of freedom. Stress-intensity factors were calculated by using a nodal-force method for distribution along the crack front and by using a compliance method for average values. The stress intensity factors and load-line displacements are presented and compared with experimental solutions from the literature. The stress intensity factors and load-line displacements were about 2.5 and 5 percent lower than the reported experimental values, respectively.

Raju, I. S.↗

NASA NTRS1985

Three-dimensional elastic-plastic finite-element analysis of fatigue crack propagation

Fatigue cracks are a major problem in designing structures subjected to cyclic loading. Cracks frequently occur in structures such as aircraft and spacecraft. The inspection intervals of many aircraft structures are based on crack-propagation lives. Therefore, improved prediction of propagation lives under flight-load conditions (variable-amplitude loading) are needed to provide more realistic design criteria for these structures. The main thrust was to develop a three-dimensional, nonlinear, elastic-plastic, finite element program capable of extending a crack and changing boundary conditions for the model under consideration. The finite-element model is composed of 8-noded (linear-strain) isoparametric elements. In the analysis, the material is assumed to be elastic-perfectly plastic. The cycle stress-strain curve for the material is shown Zienkiewicz's initial-stress method, von Mises's yield criterion, and Drucker's normality condition under small-strain assumptions are used to account for plasticity. The three-dimensional analysis is capable of extending the crack and changing boundary conditions under cyclic loading.

Goglia, G. L.↗

NASA NTRS1987

Finite element techniques for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation

Finite element procedures for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation have been implemented. For both formulations, streamline-upwind/Petrov-Galerkin techniques are used for the discretization of the transport equations. The main problem associated with the vorticity stream-function formulation is the lack of boundary conditions for vorticity at solid surfaces. Here an implicit treatment of the vorticity at no-slip boundaries is incorporated in a predictor-multicorrector time integration scheme. For the primitive variable formulation, mixed finite-element approximations are used. A nine-node element and a four-node + bubble element have been implemented. The latter is shown to exhibit a checkerboard pressure mode and a numerical treatment for this spurious pressure mode is proposed. The two methods are compared from the points of view of simulating internal and external flows and the possibilities of extensions to three dimensions.

Glaisner, F.↗

NASA NTRS1987

Finite element solution techniques for large-scale problems in computational fluid dynamics

Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global matrices. In the adaptive implicit-explicit scheme, the implicit elements are selected dynamically based on element level stability and accuracy considerations. This scheme provides implicit refinement where it is needed. The methods are applied to various problems governed by the convection-diffusion and incompressible Navier-Stokes equations. In all cases studied, the results obtained are indistinguishable from those obtained by the implicit formulations.

Liou, J.↗

NASA NTRS1986

Finite-element reentry heat-transfer analysis of space shuttle Orbiter

A structural performance and resizing (SPAR) finite-element thermal analysis computer program was used in the heat-transfer analysis of the space shuttle orbiter subjected to reentry aerodynamic heating. Three wing cross sections and one midfuselage cross section were selected for the thermal analysis. The predicted thermal protection system temperatures were found to agree well with flight-measured temperatures. The calculated aluminum structural temperatures also agreed reasonably well with the flight data from reentry to touchdown. The effects of internal radiation and of internal convection were found to be significant. The SPAR finite-element solutions agreed reasonably well with those obtained from the conventional finite-difference method.

Ko, William L.↗

NASA NTRS1986

Computational solid mechanics (finite elements and boundary elements) - Present status and future directions

Computational finite-element and boundary-element methods are reviewed, and their application to the mechanics of solids is discussed. Stability conditions for general FEMs are considered in addition to the use of least-order, stable, invariant, or hybrid/mixed isoparametric elements as alternatives to the displacement-based isoparametric elements. The use of symbolic manipulation, adaptive mesh refinement, transient dynamic response, and boundary-element methods for linear elaslticity and finite-strain problems of inelastic materials are also discussed.

Atluri, S. N.↗

NASA NTRS1988

Theory and application of radiation boundary operators

A succinct unified review is provided of the theory of radiation boundary operators. With the recent introduction of the on-surface radiation condition (OSRC) method and the continued growth of finite-difference and finite-element techniques for modeling electromagnetic wave scattering problems, the understanding and use of radiation boundary operators has become increasingly important. Results are presented to illustrate the application of radiation boundary operators in both these areas. Recent OSRC results include analysis of the scattering behavior of both electrically small and large cylinders, a reactively loaded acoustic sphere, and a simple reentrant duct. Radiation boundary operator results include the demonstration of the effectiveness of higher-order operators in truncating finite-difference time-domain grids.

Moore, Thomas G.↗

NASA NTRS1989

Multigrid solution of the Navier-Stokes equations on triangular meshes

A new Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite-element Galerkin approximation, which can be shown to be equivalent to a finite-volume approximation for regular equilateral triangular meshes. Integration to steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. The convergence efficiency of the present method is shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.

Mavriplis, D. J.↗

NASA NTRS1990

Optimum element density studies for finite-element thermal analysis of hypersonic aircraft structures

Different finite element models previously set up for thermal analysis of the space shuttle orbiter structure are discussed and their shortcomings identified. Element density criteria are established for the finite element thermal modelings of space shuttle orbiter-type large, hypersonic aircraft structures. These criteria are based on rigorous studies on solution accuracies using different finite element models having different element densities set up for one cell of the orbiter wing. Also, a method for optimization of the transient thermal analysis computer central processing unit (CPU) time is discussed. Based on the newly established element density criteria, the orbiter wing midspan segment was modeled for the examination of thermal analysis solution accuracies and the extent of computation CPU time requirements. The results showed that the distributions of the structural temperatures and the thermal stresses obtained from this wing segment model were satisfactory and the computation CPU time was at the acceptable level. The studies offered the hope that modeling the large, hypersonic aircraft structures using high-density elements for transient thermal analysis is possible if a CPU optimization technique was used.

Ko, William L.↗

NASA NTRS1990

ZIP3D: An elastic and elastic-plastic finite-element analysis program for cracked bodies

ZIP3D is an elastic and an elastic-plastic finite element program to analyze cracks in three dimensional solids. The program may also be used to analyze uncracked bodies or multi-body problems involving contacting surfaces. For crack problems, the program has several unique features including the calculation of mixed-mode strain energy release rates using the three dimensional virtual crack closure technique, the calculation of the J integral using the equivalent domain integral method, the capability to extend the crack front under monotonic or cyclic loading, and the capability to close or open the crack surfaces during cyclic loading. The theories behind the various aspects of the program are explained briefly. Line-by-line data preparation is presented. Input data and results for an elastic analysis of a surface crack in a plate and for an elastic-plastic analysis of a single-edge-crack-tension specimen are also presented.

Shivakumar, K. N.↗

NASA NTRS1991

The NASA/industry design analysis methods for vibrations (DAMVIBS) program: Accomplishments and contributions

A NASA Langley-sponsored rotorcraft structural dynamics program, known as Design Analysis Methods for VIBrationS (DAMVIBS), has been under development since 1984. The objective of this program was to establish the technology base needed by the industry to develop an advanced finite-element-based dynamics design analysis capability for vibrations. Under the program, teams from the four major helicopter manufacturers have formed finite-element models, conducted ground vibration tests, made test/analysis comparisons of both metal and composite airframes, performed 'difficult components' studies on airframes to identify components which need more complete finite-element representation for improved correlation, and evaluated industry codes for computing coupled rotor-airframe vibrations. Studies aimed at establishing the role that structural optimization can play in airframe vibrations design work have also been initiated. Five government/industry meetings were held in connection with these activities during the course of the program. Because the DAMVIBS Program is coming to an end, the fifth meeting included a brief assessment of the program and its benefits to the industry.

Kvaternik, Raymond G.↗