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High-Order Shock Fitting with Finite Element Methods

A moving-grid, shock-tracking, finite element method has been implemented that can achieve high-order accuracy for flow simulations with shocks. In this approach, element edges in the computational mesh are fitted to the shock front and moved with the shock throughout the simulation. The Euler equations are solved on the moving mesh in an arbitrary Lagrangian-Eulerian framework. Three different methods for specifying the shock motion have been tested,and the order of accuracy of the resulting solutions was verified. It was found that one of the methods is applicable only for problems with a constant upstream flow state, whereas the other two methods converge to the expected solution for general shock problems. When using a finite element method with polynomial degree p, the two general shock motion methods converged with the expected order of accuracy of (p+1). Finally, accurate solutions are obtained for supersonic nozzle and blunt body bow shock problems. Based on the results, it is concluded that the shock tracking method can preserve high-order solution accuracy in the vicinity of a shock wave.

Luke D'Aquila↗

NASA NTRS1985

Books and monographs on finite element technology

The present paper proviees a listing of all of the English books and some of the foreign books on finite element technology, taking into account also a list of the conference proceedings devoted solely to finite elements. The references are divided into categories. Attention is given to fundamentals, mathematical foundations, structural and solid mechanics applications, fluid mechanics applications, other applied science and engineering applications, computer implementation and software systems, computational and modeling aspects, special topics, boundary element methods, proceedings of symmposia and conferences on finite element technology, bibliographies, handbooks, and historical accounts.

Noor, A. K.↗

NASA NTRS2007

Simulating Space Capsule Water Landing with Explicit Finite Element Method

A study of using an explicit nonlinear dynamic finite element code for simulating the water landing of a space capsule was performed. The finite element model contains Lagrangian shell elements for the space capsule and Eulerian solid elements for the water and air. An Arbitrary Lagrangian Eulerian (ALE) solver and a penalty coupling method were used for predicting the fluid and structure interaction forces. The space capsule was first assumed to be rigid, so the numerical results could be correlated with closed form solutions. The water and air meshes were continuously refined until the solution was converged. The converged maximum deceleration predicted is bounded by the classical von Karman and Wagner solutions and is considered to be an adequate solution. The refined water and air meshes were then used in the models for simulating the water landing of a capsule model that has a flexible bottom. For small pitch angle cases, the maximum deceleration from the flexible capsule model was found to be significantly greater than the maximum deceleration obtained from the corresponding rigid model. For large pitch angle cases, the difference between the maximum deceleration of the flexible model and that of its corresponding rigid model is smaller. Test data of Apollo space capsules with a flexible heat shield qualitatively support the findings presented in this paper.

Wang, John T.↗

NASA NTRS1989

Global functions in global-local finite-element analysis of localized stresses in prismatic structures

An important consideration in the global local finite-element method (GLFEM) is the availability of global functions for the given problem. The role and mathematical requirements of these global functions in a GLFEM analysis of localized stress states in prismatic structures are discussed. A method is described for determining these global functions. Underlying this method are theorems due to Toupin and Knowles on strain energy decay rates, which are related to a quantitative expression of Saint-Venant's principle. It is mentioned that a mathematically complete set of global functions can be generated, so that any arbitrary interface condition between the finite element and global subregions can be represented. Convergence to the true behavior can be achieved with increasing global functions and finite-element degrees of freedom. Specific attention is devoted to mathematically two-dimensional and three-dimensional prismatic structures. Comments are offered on the GLFEM analysis of NASA flat panel with a discontinuous stiffener. Methods for determining global functions for other effects are also indicated, such as steady-state dynamics and bodies under initial stress.

Dong, Stanley B.↗

NASA NTRS1993

A combined experimental and finite element study to predict the failure mechanisms in SiC coated carbon/carbon composites at room and elevated temperatures under flexural loading

Response of quasi-isotropic laminates of SiC coated Carbon/Carbon (C/C) composites have been investigated under flexural loading at various temperatures. Variation of load-deflection behavior with temperatures are studied. Increase in flexural strength and stiffness are observed with the rise in temperature. Extensive analyses through Optical Microscope (OM) and Non-Destructive Evaluation (NDE) have been performed to understand the failure mechanisms. Damage zone is found only within the neighborhood of the loading plane. Isoparametric layered shell elements developed on the basis of the first order shear deformation theory have been used to model the thin laminates of C/C under flexural loading. Large deformation behavior has been considered in the finite element analysis to account for the non-linearities encountered during the actual test. Data generated using finite element analysis are presented to corroborate the experimental findings, and a comparison in respect of displacement and stress-strain behavior are given to check the accuracy of the finite element analysis. Reasonable correlation between the experimental and finite element results have been established.

Mahfuz, Hassan↗

NASA NTRS2019

Calibration of a Structural Finite Element Model for a Representative Inflatable Space Structure Utilizing Probabilistic Methods and Surrogate Models

A structural finite element model representing a novel inflatable airlock concept has been calibrated using full‐scale test data. The concept, denoted as the Non‐Axisymmetric Inflatable Pressure Structure (NAIPS), was developed under NASA’s Minimalistic Advanced Softgoods Hatch (MASH) Program. The current studies extended previous numerical efforts by incorporating the midbody section of the NAIPS to the dome section and calibrating the model with test data using a process that included surrogate models. Brief overviews of the finite element model and calibration process are provided. The completion of the calibration process provided a model that adequately replicated the test data. The successful demonstration of calibration of a finite element model representing an inflatable habitat provides confidence in the ability to use numerical simulations and associated surrogate models to support design and certification of inflatable space habitats.

Lyle, Karen H.↗

NASA NTRS1993

The p-version of the finite element method in incremental elasto-plastic analysis

Whereas the higher-order versions of the finite elements method (the p- and hp-version) are fairly well established as highly efficient methods for monitoring and controlling the discretization error in linear problems, little has been done to exploit their benefits in elasto-plastic structural analysis. Aspects of incremental elasto-plastic finite element analysis which are particularly amenable to improvements by the p-version is discussed. These theoretical considerations are supported by several numerical experiments. First, an example for which an analytical solution is available is studied. It is demonstrated that the p-version performs very well even in cycles of elasto-plastic loading and unloading, not only as compared to the traditional h-version but also in respect to the exact solution. Finally, an example of considerable practical importance - the analysis of a cold-worked lug - is presented which demonstrates how the modeling tools offered by higher-order finite element techniques can contribute to an improved approximation of practical problems.

Holzer, Stefan M.↗

NASA NTRS1993

A finite-element-based perturbation model for the rotordynamic analysis of shrouded pump impellers: Part 2: User's guide

This report describes the computational steps involved in executing a finite-element-based perturbation model for computing the rotor dynamic coefficients of a shrouded pump impeller or a simple seal. These arise from the fluid/rotor interaction in the clearance gap. In addition to the sample cases, the computational procedure also applies to a separate category of problems referred to as the 'seal-like' category. The problem, in this case, concerns a shrouded impeller, with the exception that the secondary, or leakage, passage is totally isolated from the primary-flow passage. The difference between this and the pump problem is that the former is analytically of the simple 'seal-like' configuration, with two (inlet and exit) flow-permeable stations, while the latter constitutes a double-entry / double-discharge flow problem. In all cases, the problem is that of a rotor clearance gap. The problem here is that of a rotor excitation in the form of a cylindrical whirl around the housing centerline for a smooth annular seal. In its centered operation mode, the rotor is assumed to give rise to an axisymmetric flow field in the clearance gap. As a result, problems involving longitudinal or helical grooves, in the rotor or housing surfaces, go beyond the code capabilities. Discarding, for the moment, the pre- and post-processing phases, the bulk of the computational procedure consists of two main steps. The first is aimed at producing the axisymmetric 'zeroth-order' flow solution in the given flow domain. Detailed description of this problem, including the flow-governing equations, turbulence closure, boundary conditions, and the finite-element formulation, was covered by Baskharone and Hensel. The second main step is where the perturbation model is implemented, with the input being the centered-rotor 'zeroth-order' flow solution and a prescribed whirl frequency ratio (whirl frequency divided by the impeller speed). The computational domain, in the latter case, is treated as three dimensional, with the number of computational planes in the circumferential direction being specified a priori. The reader is reminded that the deformations in the finite elements are all infinitesimally small because the rotor eccentricity itself is a virtual displacement. This explains why we have generically termed the perturbation model the 'virtually' deformable finite-element category. The primary outcome of implementing the perturbation model is the tangential and radial components, F(sub theta)(sup *) and F(sub r)(sup *) of the fluid-exerted force on the rotor surface due to the whirling motion. Repetitive execution of the perturbation model subprogram over a sufficient range of whirl frequency ratios, and subsequent interpolation of these fluid forces, using the least-square method, finally enable the user to compute the impeller rotor dynamic coefficients of the fluid/rotor interaction. These are the direct and cross-coupled stiffness, damping, and inertia effects of the fluid/rotor interaction.

Baskharone, Erian A.↗

NASA NTRS1990

Electromagnetic axisymmetric finite elements based on a gauged four-potential variational principle

Electromagnetic finite elements are derived based on a variational principle that uses the electromagnetic four-potential as a primary variable. The Lorentz gage normalization is incorporated as a constraint condition through a Lagrange multiplier field to construct elements suitable for downstream coupling with mechanical and thermal finite elements for the analysis of high-temperature superconductor devices with aerospace applications. The main advantages are: jump discontinuities on interfaces are naturally handled; no a priori approximations are invoked; and the number of degrees of freedom per node remains modest as the problem dimensionality increases. The new elements are tested on two magnetostatic axisymmetric problems. The results are in excellent agreement with analytical solutions and previous solutions for the 1D problem of a conducting infinite wire, in which case the multiplier field has no effect. For materials of widely different permeability, jump conditions are naturally accommodated by the present formulation.

Schuler, J.↗

NASA NTRS1996

A viscoelastic higher-order beam finite element

A viscoelastic internal variable constitutive theory is applied to a higher-order elastic beam theory and finite element formulation. The behavior of the viscous material in the beam is approximately modeled as a Maxwell solid. The finite element formulation requires additional sets of nodal variables for each relaxation time constant needed by the Maxwell solid. Recent developments in modeling viscoelastic material behavior with strain variables that are conjugate to the elastic strain measures are combined with advances in modeling through-the-thickness stresses and strains in thick beams. The result is a viscous thick-beam finite element that possesses superior characteristics for transient analysis since its nodal viscous forces are not linearly dependent an the nodal velocities, which is the case when damping matrices are used. Instead, the nodal viscous forces are directly dependent on the material's relaxation spectrum and the history of the nodal variables through a differential form of the constitutive law for a Maxwell solid. The thick beam quasistatic analysis is explored herein as a first step towards developing more complex viscoelastic models for thick plates and shells, and for dynamic analyses. The internal variable constitutive theory is derived directly from the Boltzmann superposition theorem. The mechanical strains and the conjugate internal strains are shown to be related through a system of first-order, ordinary differential equations. The total time-dependent stress is the superposition of its elastic and viscous components. Equations of motion for the solid are derived from the virtual work principle using the total time-dependent stress. Numerical examples for the problems of relaxation, creep, and cyclic creep are carried out for a beam made from an orthotropic Maxwell solid.

Johnson, Arthur R.↗

NASA NTRS1991

An accurate nonlinear finite element analysis and test correlation of a stiffened composite wing panel

State-of-the-art nonlinear finite element analysis techniques are evaluated by applying them to a realistic aircraft structural component. A wing panel from the V-22 tiltrotor aircraft is chosen because it is a typical modern aircraft structural component for which there is experimental data for comparison of results. From blueprints and drawings, a very detailed finite element model containing 2284 9-node Assumed Natural-Coordinate Strain elements was generated. A novel solution strategy which accounts for geometric nonlinearity through the use of corotating element reference frames and nonlinear strain-displacement relations is used to analyze this detailed model. Results from linear analyses using the same finite element model are presented in order to illustrate the advantages and costs of the nonlinear analysis as compared with the more traditional linear analysis.

Davis, D. D., Jr.↗

NASA NTRS2002

Penalty-Based Finite Element Interface Technology for Analysis of Homogeneous and Composite Structures

An effective and robust interface element technology able to connect independently modeled finite element subdomains has been developed. This method is based on the use of penalty constraints and allows coupling of finite element models whose nodes do not coincide along their common interface. Additionally, the present formulation leads to a computational approach that is very efficient and completely compatible with existing commercial software. A significant effort has been directed toward identifying those model characteristics (element geometric properties, material properties, and loads) that most strongly affect the required penalty parameter, and subsequently to developing simple 'formulae' for automatically calculating the proper penalty parameter for each interface constraint. This task is especially critical in composite materials and structures, where adjacent sub-regions may be composed of significantly different materials or laminates. This approach has been validated by investigating a variety of two-dimensional problems, including composite laminates.

Averill, Ronald C.↗

NASA NTRS2013

Coupled Vortex-Lattice Flight Dynamic Model with Aeroelastic Finite-Element Model of Flexible Wing Transport Aircraft with Variable Camber Continuous Trailing Edge Flap for Drag Reduction

This paper presents a coupled vortex-lattice flight dynamic model with an aeroelastic finite-element model to predict dynamic characteristics of a flexible wing transport aircraft. The aircraft model is based on NASA Generic Transport Model (GTM) with representative mass and stiffness properties to achieve a wing tip deflection about twice that of a conventional transport aircraft (10% versus 5%). This flexible wing transport aircraft is referred to as an Elastically Shaped Aircraft Concept (ESAC) which is equipped with a Variable Camber Continuous Trailing Edge Flap (VCCTEF) system for active wing shaping control for drag reduction. A vortex-lattice aerodynamic model of the ESAC is developed and is coupled with an aeroelastic finite-element model via an automated geometry modeler. This coupled model is used to compute static and dynamic aeroelastic solutions. The deflection information from the finite-element model and the vortex-lattice model is used to compute unsteady contributions to the aerodynamic force and moment coefficients. A coupled aeroelastic-longitudinal flight dynamic model is developed by coupling the finite-element model with the rigid-body flight dynamic model of the GTM.

Flexible Aicraft↗

NASA NTRS1992

Least-squares finite element solution of 3D incompressible Navier-Stokes problems

Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.

Jiang, Bo-Nan↗

NASA NTRS1983

Two-dimensional Finite Element Modeling for Modeling Tectonic Stress and Strain

Techniques of finite element analysis in two dimensional plane strain were applied to problems of geophysics and tectonics. More specifically, the flexibility of the finite element method was employed to address problems involving geological complexity and fault interactions. The modeling of effective anisotropy in material elastic properties proved useful in describing the deformation of faulted crustal blocks. The applications of this modeling work to problems of actual tectonics in southern California was explored. Preliminary models show encouraging agreement with measured tectonic strain in this region, and modeling work was done to gain an understanding of the stress state in a locked fault region with future seismic potential.

Lyzenga, G. A.↗

NASA NTRS1996

Finite Element Analysis of a NASA National Transonic Facility Wind Tunnel Balance

This paper presents the results of finite element analyses and correlation studies performed on a NASA National Transonic Facility (NTF) Wind Tunnel balance. In the past NASA has relied primarily on classical hand analyses, coupled with relatively large safety factors, for predicting maximum stresses in wind tunnel balances. Now, with the significant advancements in computer technology and sophistication of general purpose analysis codes, it is more reasonable to pursue finite element analyses of these balances. The correlation studies of the present analyses show very good agreement between the analyses and data measured with strain gages and therefore the studies give higher confidence for using finite element analyses to analyze and optimize balance designs in the future.

Lindell, Michael C.↗

NASA NTRS1999

Finite Element Analysis of a NASA National Transonic Facility Wide Tunnel Balance

Lindell, Michael C.↗

NASA NTRS1980

TAP 2: A finite element program for thermal analysis of convectively cooled structures

A finite element computer program (TAP 2) for steady-state and transient thermal analyses of convectively cooled structures is presented. The program has a finite element library of six elements: two conduction/convection elements to model heat transfer in a solid, two convection elements to model heat transfer in a fluid, and two integrated conduction/convection elements to represent combined heat transfer in tubular and plate/fin fluid passages. Nonlinear thermal analysis due to temperature-dependent thermal parameters is performed using the Newton-Raphson iteration method. Transient analyses are performed using an implicit Crank-Nicolson time integration scheme with consistent or lumped capacitance matrices as an option. Program output includes nodal temperatures and element heat fluxes. Pressure drops in fluid passages may be computed as an option. User instructions and sample problems are presented in appendixes.

Thornton, E. A.↗