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At least 739 records · Page 41

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NASA NTRS1986

A spectral element method for the simulation of unsteady incompressible flows with heat transfer

The spectral element method is a high-order finite element technique for solution of the Navier-Stokes and energy equations. In the isoparametric spectral element discretization, the domain is broken up into general brick elements, and the dependent and independent variables represented as high-order tensor-product Lagrangian interpolants through Chebyshev collocation points. The nonlinear and convective terms in the governing equations are treated with explicit collocation, while the pressure and diffusive contributions are handled implicitly using variational projection operators. The method is applied to flow past a cylinder, flow in grooved channels, and natural convection in an enclosure.

Karniadakis, George E.↗

NASA NTRS1987

A microstructural lattice model for strain oriented problems: A combined Monte Carlo finite element technique

A specialized, microstructural lattice model, termed MCFET for combined Monte Carlo Finite Element Technique, was developed which simulates microstructural evolution in material systems where modulated phases occur and the directionality of the modulation is influenced by internal and external stresses. In this approach, the microstructure is discretized onto a fine lattice. Each element in the lattice is labelled in accordance with its microstructural identity. Diffusion of material at elevated temperatures is simulated by allowing exchanges of neighboring elements if the exchange lowers the total energy of the system. A Monte Carlo approach is used to select the exchange site while the change in energy associated with stress fields is computed using a finite element technique. The MCFET analysis was validated by comparing this approach with a closed form, analytical method for stress assisted, shape changes of a single particle in an infinite matrix. Sample MCFET analytical for multiparticle problems were also run and in general the resulting microstructural changes associated with the application of an external stress are similar to that observed in Ni-Al-Cr alloys at elevated temperature.

Gayda, J.↗

NASA NTRS1987

Design of an elemental analysis system for CELSS research

The results of experiments conducted with higher plants in tightly sealed growth chambers provide definite evidence that the physical closure of a chamber has significant effects on many aspects of a plant's biology. One of these effects is seen in the change in rates of uptake, distribution, and re-release or nutrient elements by the plant (mass balance). Experimental data indicates that these rates are different from those recorded for plants grown in open field agriculture, or in open growth chambers. Since higher plants are a crucial component of a controlled ecological life support system (CELSS), it is important that the consequences of these rate differences be understood with regard to the growth and yield of the plants. A description of a system for elemental analysis which can be used to monitor the mass balance of nutrient elements in CELSS experiments is given. Additionally, data on the uptake of nutrient elements by higher plants grown in a growth chamber is presented.

Schwartzkopf, Steven H.↗

NASA NTRS1987

Strain-energy-release rate analysis of the end-notched flexure specimen using the finite-element method

Two-dimensional finite-element analysis of the end-notched flexure specimen was performed using 8-node isoparametric, parabolic elements to evaluate compliance and mode II strain energy release rates, G sub II. The G sub II values were computed using two different techniques: the virtural crack-closure technique (VCCT) and the rate of change of compliance with crack length (compliance derivative method). The analysis was performed for various crack-length-to-semi-span (a/L) ratios ranging from 0.2 to 0.9. Three material systems representing a wide range of material properties were analyzed. The compliance and strain energy release rates of the specimen calculated with the present finite-element analysis agree very well with beam theory equations including transverse shear. The G sub II values calculated using the compliance derivative method compared extremely well with those calculated using the VCCT. The G sub II values obtained by the compliance derivative method using the top or bottom beam deflections agreed closely with each other. The strain energy release rates from a plane-stress analysis were higher than the plane-strain values by only a small percentage, indicating that either assumption may be used in the analysis. The G sub II values for one material system calculated from the finite-element analysis agreed with one solution in the literature and disagreed with the other solution in the literature.

Salpekar, S. A.↗

NASA NTRS1988

Consistent linearization of the element-independent corotational formulation for the structural analysis of general shells

A consistent linearization is provided for the element-dependent corotational formulation, providing the proper first and second variation of the strain energy. As a result, the warping problem that has plagued flat elements has been overcome, with beneficial effects carried over to linear solutions. True Newton quadratic convergence has been restored to the Structural Analysis of General Shells (STAGS) code for conservative loading using the full corotational implementation. Some implications for general finite element analysis are discussed, including what effect the automatic frame invariance provided by this work might have on the development of new, improved elements.

Rankin, C. C.↗

NASA NTRS1988

Improved finite strip Mindlin plate bending element using assumed shear strain distributions

A linear finite strip plate element based on Mindlin/Reissner plate theory is developed. The analysis is suitable for both thin and thick plates. In the formulation new transverse shear strains are introduced and assumed constant in each two-code linear strip. The element stiffness matrix is explicitly formulated for efficient computation and computer implementation. Numerical results showing the efficiency and predictive capability of the element for the analysis of plates are presented for different support and loading conditions and a wide range of thicknesses. No sign of shear locking phenomenon was observed with the newly developed element.

Chulya, Abhisak↗

NASA NTRS1988

An error estimation procedure for plate bending elements

Procedures for identifying and eliminating errors inherent in individual finite elements and those due to the discretization of the continuum are presented. The elemental errors are identified through the use of an element formulation procedure based on physically interpretable strain gradient interpolation functions. The use of physically interpretable notation allows these errors to be eliminated using rational arguments. The discretization errors are identified by comparing the finite-element solution with a smoothed superconvergent solution. The errors thus identified are used to guide an adaptive mesh refinement procedure which produces improved results.

Dow, John O.↗

NASA NTRS1988

Temperature and composition dependencies of trace element partitioning - Olivine/melt and low-Ca pyroxene/melt

This paper presents a systematic thermodynamic analysis of the effects of temperature and composition on olivine/melt and low-Ca pyroxene/melt partitioning. Experiments were conducted in several synthetic basalts with a wide range of Fe/Mg, determining partition coefficients for Eu, Ca, Mn, Fe, Ni, Sm, Cd, Y, Yb, Sc, Al, Zr, and Ti and modeling accurately the changes in free energy for trace element exchange between crystal and melt as functions of the trace element size and charge. On the basis of this model, partition coefficients for olivine/melt and low-Ca pyroxene/melt can be predicted for a wide range of elements over a variety of basaltic bulk compositions and temperatures. Moreover, variations in partition coeffeicients during crystallization or melting can be modeled on the basis of changes in temperature and major element chemistry.

Colson, R. O.↗

NASA NTRS1988

A new hybrid transfinite element computational methodology for applicability to conduction/convection/radiation heat transfer

This paper describes new and recent advances in the development of a hybrid transfinite element computational methodology for applicability to conduction/convection/radiation heat transfer problems. The transfinite element methodology, while retaining the modeling versatility of contemporary finite element formulations, is based on application of transform techniques in conjunction with classical Galerkin schemes and is a hybrid approach. The purpose of this paper is to provide a viable hybrid computational methodology for applicability to general transient thermal analysis. Highlights and features of the methodology are described and developed via generalized formulations and applications to several test problems. The proposed transfinite element methodology successfully provides a viable computational approach and numerical test problems validate the proposed developments for conduction/convection/radiation thermal analysis.

Tamma, Kumar K.↗

NASA NTRS1988

An adaptive remeshing method for finite element thermal analysis

A finite element remeshing approach that makes use of quadrilateral and triangular elements is described. The approach uses the solution on a previous mesh to create a new mesh. Meshes are completely unstructured with highly refined elements in regions of steep gradients and larger elements where gradients are smaller. Studies of convergence rates for heat conduction problems with exact solutions show that for problems with highly localized solution variations, the remeshing approach gives smaller solution errors with fewer unknowns than refinement of uniform, structured meshes.

Thornton, Earl A.↗

NASA NTRS1989

Finite element modeling of frictionally restrained composite interfaces

The use of special interface finite elements to model frictional restraint in composite interfaces is described. These elements simulate Coulomb friction at the interface, and are incorporated into a standard finite element analysis of a two-dimensional isolated fiber pullout test. Various interfacial characteristics, such as the distribution of stresses at the interface, the extent of slip and delamination, load diffusion from fiber to matrix, and the amount of fiber extraction or depression are studied for different friction coefficients. The results are compared to those obtained analytically using a singular integral equation approach, and those obtained by assuming a constant interface shear strength. The usefulness of these elements in micromechanical modeling of fiber-reinforced composite materials is highlighted.

Ballarini, Roberto↗

NASA NTRS1989

On finite element implementation and computational techniques for constitutive modeling of high temperature composites

The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.

Saleeb, A. F.↗

NASA NTRS1989

Control of the errors of discretization and idealization in finite element analysis

Understanding of the basic principles which control errors of discretization in finite element analysis has increased very substantially since 1980. The main milestones were: (1) development of the theoretical basis of p-extensions (1981); (2) understanding of the proper interplay between mesh design and assignment of polynomial degree to elements. Practical realization of exponential convergence rates, independently of the smoothness of the exact solution (1984); and (3) industrial experience with the new finite element technology known as the p- or hp-version of the finite element method: General Dynamics reported thirty- to forty-fold savings in terms of human time and large savings in computer time (1986). Lockheed reported favorably on their evaluation of error estimation and quality control capabilities of the p-version in industrial settings (1987). The gains in our understanding of how to control the errors of discretization represent only half of the control necessary to ensure that a numerical model is in fact an accurate representation of the corresponding physical system. Control of the errors of idealization is equally important. A brief overview of the main ideas of how to ensure the quality and reliability of mathematical models of structural systems is presented.

Szabo, Barna A.↗

NASA NTRS1988

Realizable feed-element patterns and optimum aperture efficiency in multibeam antenna systems

The results of an earlier paper by Rahmat-Samii et al. (1981), regarding realizable patterns from feed elements that are part of an array that feeds a reflector antenna, are extended. The earlier paper used a cos exp q theta model for the element radiation pattern, whereas here a parametric study is performed, using a model that assumes a central beam of cos exp q theta shape, with a constant sidelobe level outside the central beam. Realizable q-values are constrained by the maximum directivity based on feed element area. The optimum aperture efficiency (excluding array feed network losses) in an array-reflector system is evaluated as a function of element spacing using this model as well as the model of the earlier paper. Experimental data for tapered slot antenna (TSA) arrays are in agreement with the conclusions based on the model.

Yngvesson, K. S.↗

NASA NTRS1988

Strain energy release rate analysis of the end-notched flexure specimen using the finite-element method

Two-dimensional finite-element analysis of the end-notched flexure specimen was performed using 8-node isoparametric, parabolic elements to evaluate compliance and mode II strain energy release rates, G sub II. The G sub II values were computed using two different techniques: the virtual crack-closure technique (VCCT) and the rate of change of compliance with crack length (compliance derivative method). The analysis was performed for various crack-length-to-semi-span (a/L) ratios ranging from 0.2 to 0.9. Three material systems representing a wide range of material properties were analyzed. The compliance and strain energy release rates of the specimen calculated with the present finite-element analysis agree very well with beam theory equations including transverse shear. The G sub II values calculated using the compliance derivative method compared extremely well with those calculated using the VCCT. The G sub II values obtained by the compliance derivative method using the top or bottom beam deflections agreed closely with each other. The strain energy release rates from a plane-stress analysis were higher than the plane-strain values by only a small percentage, indicating that either assumption may be used in the analysis. The G sub II values for one material system calculated from the finte-element analysis agreed with one solution in the literature and disagreed with the other solution in the literature.

Salpekar, S. A.↗

NASA NTRS1989

Thermal-structural finite element analysis using linear flux formulation

A linear flux approach is developed for a finite element thermal-structural analysis of steady-state thermal and structural problems. The element fluxes are assumed to vary linearly in the same form as the element unknown variables, and the finite element matrices are evaluated in closed form. Since numerical integration is avoided, significant computational time saving is achieved. Solution accuracy and computational speed improvements are demonstrated by solving several two-and three-dimensional thermal-structural examples.

Pandey, Ajay K.↗

NASA NTRS1989

Eigensolution of finite element problems in a completely connected parallel architecture

A parallel algorithm is presented for the solution of the generalized eigenproblem in linear elastic finite element analysis. The algorithm is based on a completely connected parallel architecture in which each processor is allowed to communicate with all other processors. The algorithm is successfully implemented on a tightly coupled MIMD parallel processor. A finite element model is divided into m domains each of which is assumed to process n elements. Each domain is then assigned to a processor or to a logical processor (task) if the number of domains exceeds the number of physical processors. The effect of the number of domains, the number of degrees-of-freedom located along the global fronts, and the dimension of the subspace on the performance of the algorithm is investigated. For a 64-element rectangular plate, speed-ups of 1.86, 3.13, 3.18, and 3.61 are achieved on two, four, six, and eight processors, respectively.

Akl, F.↗

NASA NTRS1989

Error analysis of finite element solutions for postbuckled cylinders

A general method of error analysis and correction is investigated for the discrete finite-element results for cylindrical shell structures. The method for error analysis is an adaptation of the method of successive approximation. When applied to the equilibrium equations of shell theory, successive approximations derive an approximate continuous solution from the discrete finite-element results. The advantage of this continuous solution is that it contains continuous partial derivatives of an order higher than the basis functions of the finite-element solution. Preliminary numerical results are presented in this paper for the error analysis of finite-element results for a postbuckled stiffened cylindrical panel modeled by a general purpose shell code. Numerical results from the method have previously been reported for postbuckled stiffened plates. A procedure for correcting the continuous approximate solution by Newton's method is outlined.

Sistla, Rajaram↗