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At least 1,135 records · Page 63

Finite element solution of optimal control problems with state-control inequality constraints

It is demonstrated that the weak Hamiltonian finite-element formulation is amenable to the solution of optimal control problems with inequality constraints which are functions of both state and control variables. Difficult problems can be treated on account of the ease with which algebraic equations can be generated before having to specify the problem. These equations yield very accurate solutions. Owing to the sparse structure of the resulting Jacobian, computer solutions can be obtained quickly when the sparsity is exploited.

Bless, Robert R.↗

Theoretical and numerical difficulties in 3-D vector potential methods in finite element magnetostatic computations

This paper describes the results of application of three well known 3D magnetic vector potential (MVP) based finite element formulations for computation of magnetostatic fields in electrical devices. The three methods were identically applied to three practical examples, the first of which contains only one medium (free space), while the second and third examples contained a mix of free space and iron. The first of these methods is based on the unconstrained curl-curl of the MVP, while the second and third methods are predicated upon constraining the divergence of the MVP 10 zero (Coulomb's Gauge). It was found that the two latter methods cease to give useful and meaningful results when the global solution region contains a mix of media of high and low permeabilities. Furthermore, it was found that their results do not achieve the intended zero constraint on the divergence of the MVP.

Demerdash, N. A.↗

Elastic-plastic finite element analyses of an unidirectional, 9 vol percent tungsten fiber reinforced copper matrix composite

Micromechanical modeling via elastic-plastic finite element analyses were performed to investigate the effects that the residual stresses and the degree of matrix work hardening (i.e., cold-worked, annealed) have upon the behavior of a 9 vol percent, unidirectional W/Cu composite, undergoing tensile loading. The inclusion of the residual stress-containing state as well as the simulated matrix material conditions proved to be significant since the Cu matrix material exhibited plastic deformation, which affected the subsequent tensile response of the composite system. The stresses generated during cooldown to room temperature from the manufacturing temperature were more of a factor on the annealed-matrix composite, since they induced the softened matrix to plastically flow. This event limited the total load-carrying capacity of this matrix-dominated, ductile-ductile type material system. Plastic deformation of the hardened-matrix composite during the thermal cooldown stage was not considerable, therefore, the composite was able to sustain a higher stress before showing any appreciable matrix plasticity. The predicted room temperature, stress-strain response, and deformation stages under both material conditions represented upper and lower bounds characteristic of the composite's tensile behavior. The initial deformation stage for the hardened material condition showed negligible matrix plastic deformation while for the annealed state, its initial deformation stage showed extensive matrix plasticity. Both material conditions exhibited a final deformation stage where the fiber and matrix were straining plastically. The predicted stress-strain results were compared to the experimental, room temperature, tensile stress-strain curve generated from this particular composite system. The analyses indicated that the actual thermal-mechanical state of the composite's Cu matrix, represented by the experimental data, followed the annealed material condition.

Sanfeliz, Jose G.↗

Solution of elastic-plastic stress analysis problems by the p-version of the finite element method

The solution of small strain elastic-plastic stress analysis problems by the p-version of the finite element method is discussed. The formulation is based on the deformation theory of plasticity and the displacement method. Practical realization of controlling discretization errors for elastic-plastic problems is the main focus. Numerical examples which include comparisons between the deformation and incremental theories of plasticity under tight control of discretization errors are presented.

Szabo, Barna A.↗

Highly Accurate Beam Torsion Solutions Using the p-Version Finite Element Method

A new treatment of the classical beam torsion boundary value problem is applied. Using the p-version finite element method with shape functions based on Legendre polynomials, torsion solutions for generic cross-sections comprised of isotropic materials are developed. Element shape functions for quadrilateral and triangular elements are discussed, and numerical examples are provided.

Smith, James P.↗

Finite Element Simulation of a Space Shuttle Solid Rocket Booster Aft Skirt Splashdown Using an Arbitrary Lagrangian-eulerian Approach

Explicit finite element techniques employing an Arbitrary Lagrangian-Eulerian (ALE) methodology, within the transient dynamic code LS-DYNA, are used to predict splashdown loads on a proposed replacement/upgrade of the hydrazine tanks on the thrust vector control system housed within the aft skirt of a Space Shuttle Solid Rocket Booster. Two preliminary studies are performed prior to the full aft skirt analysis: An analysis of the proposed tank impacting water without supporting aft skirt structure, and an analysis of space capsule water drop tests conducted at NASA's Langley Research Center. Results from the preliminary studies provide confidence that useful predictions can be made by applying the ALE methodology to a detailed analysis of a 26-degree section of the skirt with proposed tank attached. Results for all three studies are presented and compared to limited experimental data. The challenges of using the LS-DYNA ALE capability for this type of analysis are discussed.

Melis, Matthew E.↗

Parallel Finite Element Domain Decomposition for Structural/Acoustic Analysis

A domain decomposition (DD) formulation for solving sparse linear systems of equations resulting from finite element analysis is presented. The formulation incorporates mixed direct and iterative equation solving strategics and other novel algorithmic ideas that are optimized to take advantage of sparsity and exploit modern computer architecture, such as memory and parallel computing. The most time consuming part of the formulation is identified and the critical roles of direct sparse and iterative solvers within the framework of the formulation are discussed. Experiments on several computer platforms using several complex test matrices are conducted using software based on the formulation. Small-scale structural examples are used to validate thc steps in the formulation and large-scale (l,000,000+ unknowns) duct acoustic examples are used to evaluate the ORIGIN 2000 processors, and a duster of 6 PCs (running under the Windows environment). Statistics show that the formulation is efficient in both sequential and parallel computing environmental and that the formulation is significantly faster and consumes less memory than that based on one of the best available commercialized parallel sparse solvers.

Nguyen, Duc T.↗

SUPG Finite Element Simulations of Compressible Flows for Aerothermodynamic Applications

This viewgraph presentation reviews the Streamline-Upwind Petrov-Galerkin (SUPG) Finite Element Simulation. It covers the background, governing equations, weak formulation, shock capturing, inviscid flux discretization, time discretization, linearization, and implicit solution strategies. It also reviews some applications such as Type IV Shock Interaction, Forward-Facing Cavity and AEDC Sharp Double Cone.

Kirk, Benjamin S.↗

Cyclic Symmetry Finite Element Forced Response Analysis of a Distortion-Tolerant Fan with Boundary Layer Ingestion

Accurate prediction of the blade vibration stress is required to determine overall durability of fan blade design under Boundary Layer Ingestion (BLI) distorted flow environments. Traditional single blade modeling technique is incapable of representing accurate modeling for the entire rotor blade system subject to complex dynamic loading behaviors and vibrations in distorted flow conditions. A particular objective of our work was to develop a high-fidelity full-rotor aeromechanics analysis capability for a system subjected to a distorted inlet flow by applying cyclic symmetry finite element modeling methodology. This reduction modeling method allows computationally very efficient analysis using a small periodic section of the full rotor blade system. Experimental testing by the use of the 8-foot by 6-foot Supersonic Wind Tunnel Test facility at NASA Glenn Research Center was also carried out for the system designated as the Boundary Layer Ingesting Inlet/Distortion-Tolerant Fan (BLI2DTF) technology development. The results obtained from the present numerical modeling technique were evaluated with those of the wind tunnel experimental test, toward establishing a computationally efficient aeromechanics analysis modeling tool facilitating for analyses of the full rotor blade systems subjected to a distorted inlet flow conditions. Fairly good correlations were achieved hence our computational modeling techniques were fully demonstrated. The analysis result showed that the safety margin requirement set in the BLI2DTF fan blade design provided a sufficient margin with respect to the operating speed range.

forced response analysis↗

Convergence rates for finite element problems with singularities. Part 1: Antiplane shear

The problem of a finite crack in an infinite medium under antiplane shear load is considered. It is shown that the nodal forces at the tip of the crack accurately gives the order of singularity, that n energy release methods can give the strength to better than 1 percent with element size 1/10 the crack length, and that nodal forces give a much better estimate of the stress field than do the elements themselves. The finite element formulation and the factoring of tridiagonal matrices are discussed.

Plunkett, R.↗

Prediction of the bulk temperature in spur gears based on finite element temperature analysis

The temperature distribution in spur gears operating in a state of thermal equilibrium is solved by using a finite element method. The effects of various dimensionless parameters on bulk temperature are shown. A table is provided which can be used to predict the bulk temperature on gear teeth, once the heat transfer coefficients and frictional heat input is estimated. Theoretical results for estimating heat transfer coefficients and frictional heat are also summarized.

Patir, N.↗

Engine dynamic analysis with general nonlinear finite element codes. II - Bearing element implementation, overall numerical characteristics and benchmarking

Second-year efforts within a three-year study to develop and extend finite element (FE) methodology to efficiently handle the transient/steady state response of rotor-bearing-stator structure associated with gas turbine engines are outlined. The two main areas aim at (1) implanting the squeeze film damper element into a general purpose FE code for testing and evaluation; and (2) determining the numerical characteristics of the FE-generated rotor-bearing-stator simulation scheme. The governing FE field equations are set out and the solution methodology is presented. The choice of ADINA as the general-purpose FE code is explained, and the numerical operational characteristics of the direct integration approach of FE-generated rotor-bearing-stator simulations is determined, including benchmarking, comparison of explicit vs. implicit methodologies of direct integration, and demonstration problems.

Padovan, J.↗

A refined mixed shear flexible finite element for the nonlinear analysis of laminated plates

The present study is concerned with the development of a mixed shear flexible finite element with relaxed continuity for the geometrically linear and nonlinear analysis of laminated anisotropic plates. The formulation of the element is based on a refined higher-order theory. This theory satisfies the zero transverse shear stress boundary conditions on the top and bottom faces of the plate. Shear correction coefficients are not needed. The developed element consists of 11 degrees-of-freedom per node, taking into account three displacements, two rotations, and six moment resultants. An evaluation of the element is conducted with respect to the accuracy obtained in the bending of laminated anistropic rectangular plates with different lamination schemes, loadings, and boundary conditions.

Putcha, N. S.↗

An integrated finite element model of edge-delamination analysis for laminates due to tension, bending, and torsion loads

A two-dimensional finite-element model has been developed to calculate interlaminar stresses and strain energy release rates for the study of delamination in composite laminates subjected to various loads. This paper addresses the formulation, implementation, and verification of a suitable 'element for uniaxial tension, bending, and torsion', as well as parametric studies of the interlaminar stresses and strain energy release rates for various composite laminates. The study concentrates on establishing relationships of GI, GII, and GIII as functions of crack length and stacking sequence in laminates due to bending. Preliminary results of laminates subjected to torsional loads are included to increase the applicability and completeness of the present formulation.

Chan, W. S.↗

Finite element discrete ordinates method for radiative transfer in non-rotationally invariant scattering media - Application to the leaf canopy problem

A finite element discrete ordinates method for solving the radiative transfer equation in nonrotationally invariant scattering media has been applied to the lead-canopy problem, and results are presented on the cross sections and the reflection functions. The method is based on a unique implementation of the Galerkin integral law formulation of the transport equation. For both near-normal and grazing incidences, the transfer functions of leaf canopies are found to be strongly anisotropic, with relatively more scattered flux in the vertical directions. It is suggested that the assumption of isotropic scattering in leaf canopies is not valid.

Myneni, Ranga B.↗