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NASA NTRS1987

Approaches to the automatic generation and control of finite element meshes

The algorithmic approaches being taken to the development of finite element mesh generators capable of automatically discretizing general domains without the need for user intervention are discussed. It is demonstrated that because of the modeling demands placed on a automatic mesh generator, all the approaches taken to date produce unstructured meshes. Consideration is also given to both a priori and a posteriori mesh control devices for automatic mesh generators as well as their integration with geometric modeling and adaptive analysis procedures.

Shephard, Mark S.↗

NASA NTRS1990

Turbulent flow calculations using unstructured and adaptive meshes

A method of efficiently computing turbulent compressible flow over complex two dimensional configurations is presented. The method makes use of fully unstructured meshes throughout the entire flow-field, thus enabling the treatment of arbitrarily complex geometries and the use of adaptive meshing techniques throughout both viscous and inviscid regions of flow-field. Mesh generation is based on a locally mapped Delaunay technique in order to generate unstructured meshes with highly-stretched elements in the viscous regions. The flow equations are discretized using a finite element Navier-Stokes solver, and rapid convergence to steady-state is achieved using an unstructured multigrid algorithm. Turbulence modeling is performed using an inexpensive algebraic model, implemented for use on unstructured and adaptive meshes. Compressible turbulent flow solutions about multiple-element airfoil geometries are computed and compared with experimental data.

Mavriplis, Dimitri J.↗

NASA NTRS1990

Development of UMARC (University of Maryland Advanced Rotorcraft Code)

The University of Maryland Advanced Rotorcraft Code (UMARC) is a user-friendly, FEM-based comprehensive helicopter rotor simulation code of high numerical robustness and computational efficiency. UMARC formulates the rotor-fuselage equations using Hamilton's principle, and are discretized using finite elements in space and time. The FEM formulation allows the code to analyze a wide variety of rotor designs. Dynamic inflow modeling is used for unsteady wake inflow computations. Predicted stability, response, and blade-load data are validated with experimental data for several configurations, including representative articulated, hingeless, and bearingless rotors.

Bir, Gunjit↗

NASA NTRS1991

Turbulent flow calculations using unstructured and adaptive meshes

A method of efficiently computing turbulent compressible flow over complex two dimensional configurations is presented. The method makes use of fully unstructured meshes throughout the entire flow field, thus enabling the treatment of arbitrarily complex geometries and the use of adaptive meshing techniques throughout both viscous and inviscid regions of the flow field. Mesh generation is based on a locally mapped Delaunay technique in order to generate unstructured meshes with highly-stretched elements in the viscous regions. The flow equations are discretized using a finite element Navier-Stokes solver, and rapid convergence to steady-state is achieved using an unstructured multigrid algorithm. Turbulence modeling is performed using an inexpensive algebraic model, implemented for use on unstructured and adaptaive meshes. Compressible turbulent flow solutions about multiple-element airfoil geometries are computed and compared with expeirmental data.

Mavriplis, Dimitri J.↗

NASA NTRS1996

Simulation of Two-Fluid Flows by the Least-Squares Finite Element Method Using a Continuum Surface Tension Model

In this paper a numerical procedure for simulating two-fluid flows is presented. This procedure is based on the Volume of Fluid (VOF) method proposed by Hirt and Nichols and the continuum surface force (CSF) model developed by Brackbill, et al. In the VOF method fluids of different properties are identified through the use of a continuous field variable (color function). The color function assigns a unique constant (color) to each fluid. The interfaces between different fluids are distinct due to sharp gradients of the color function. The evolution of the interfaces is captured by solving the convective equation of the color function. The CSF model is used as a means to treat surface tension effect at the interfaces. Here a modified version of the CSF model, proposed by Jacqmin, is used to calculate the tension force. In the modified version, the force term is obtained by calculating the divergence of a stress tensor defined by the gradient of the color function. In its analytical form, this stress formulation is equivalent to the original CSF model. Numerically, however, the use of the stress formulation has some advantages over the original CSF model, as it bypasses the difficulty in approximating the curvatures of the interfaces. The least-squares finite element method (LSFEM) is used to discretize the governing equation systems. The LSFEM has proven to be effective in solving incompressible Navier-Stokes equations and pure convection equations, making it an ideal candidate for the present applications. The LSFEM handles all the equations in a unified manner without any additional special treatment such as upwinding or artificial dissipation. Various bench mark tests have been carried out for both two dimensional planar and axisymmetric flows, including a dam breaking, oscillating and stationary bubbles and a conical liquid sheet in a pressure swirl atomizer.

Wu, Jie↗

NASA NTRS2019

Benchmarking Mixed Mode Failure in Progressive Damage and Failure Analysis Methods

The verification and validation of progressive-damage-analysis finite element methods are difficult but critical tasks to undertake during their development. Verification exercises assess whether a predictive analysis tool produces results that are consistent with the fundamental concepts and assumptions of the tool under evaluation. Ideally, closed-form analytical solutions can be derived for which method verification results can be compared. Problems selected for computational tool verification are often simple and isolate individual features of the tool. In the case of progressive damage finite element methods, verifications should be performed to evaluate the ability of the model to predict the initiation of damage and its growth through the finite element mesh under a variety of conditions. Mabson et al. proposed a test case of a unidirectional, fiber-reinforced plate with a center crack subjected to tensile loads to evaluate matrix crack propagation predictions. The problem was modeled using the Abaqus Hashin continuum damage mechanics (CDM) model for fiber-reinforced composites. Different combinations of matrix strengths and element sizes were used in the simulations, and the results were compared to a closed-form solution based on linear elastic fracture mechanics (LEFM). It was determined that the Abaqus CDM model could predict the LEFM solution of Mode I cracks only when the finite element mesh density met specific requirements based on the material properties. This paper presents closed-form LEFM solutions for a center notch mixed mode (CNMM) verification problem. Parametric finite element analyses were developed using progressive damage analysis methods of both the Discrete Damage Mechanics (DDM) and CDM classes. The progressive damage analysis methods applied in the analyses of the CNMM problem include CompDam and the Floating Node Method. Analyses were conducted with various mode mixities and element sizes to verify that the damage models were working as intended and to identify any limits of applicability.

Leone, Frank↗

NASA NTRS1982

Computation of the steady viscous flow over a tri-element 'augmentor wing' airfoil

The augmentor wing consists of a main airfoil with a slotted trailing edge for blowing, and two smaller aft airfoils which shroud the jet. This configuration has been modeled for numerical simulation by a novel discretization procedure which generates four separate grids: three surface-oriented airfoil grids and one outer free-stream grid. Grid lines and slopes are continuous across boundaries, so grid overlap at common boundaries provides boundary information without interpolation. A two-dimensional unsteady thin-layer Navier-Stokes code is used to calculate the flow for the no-blowing case at freestream Mach number = 0.7, Re = 12,600.000, and angles-of-incidence = 1.05 deg. Qualitative agreement with experimental data indicates the utility of this procedure in the analysis of multi-element configurations.

Lasinski, T. A.↗

NASA NTRS2019

Verification and Validation of a Three-Dimensional Composite Impact Model with Tabulated Input

A material model which incorporates several key capabilities which have been identified by the aerospace community as lacking in the composite impact models currently available in the commercial transient dynamic finite element code LS-DYNA® has been developed. The material model utilizes experimentally based tabulated input to define the evolution of plasticity and damage as opposed to specifying discrete input parameters (such as modulus and strength. The plasticity portion of the orthotropic, three-dimensional, macroscopic composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function with a non-associative flow rule. The capability to account for the rate and temperature dependent deformation response of composites has also been incorporated into the material model. For the damage model, a strain equivalent formulation is utilized to allow for the uncoupling of the deformation and damage analyses. In the damage model, a diagonal damage tensor is defined to account for the directionally dependent variation of damage. However, the terms in the damage matrix are semi-coupled such that the damage in a particular coordinate direction is a function of the stresses and plastic strains in all of the coordinate directions. For the failure model, a tabulated approach is utilized in which a stress or strain based invariant is defined as a function of the location of the current stress state in stress space to define the initiation of failure, which allows an arbitrarily shaped failure surface to be defined. A systematic series of validation and verification studies, at a variety of length scales ranging from single element simulations to simulations of a flat panel impact test, have been performed to fully exercise and evaluate the capabilities of the developed model.

Impact↗

NASA NTRS1984

Methods for analysis of cracks in three-dimensional solids

Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.

Raju, I. S.↗

NASA NTRS1988

Theoretical studies on flapped delta wings

The effects of leading edge flaps on the aerodynamic characteristics of a low aspect-ratio delta wing are studied theoretically. As an extension of the classical crossflow plane analysis and in order to include separated shear layers, an analogy between three dimensional steady conical and two dimensional unsteady self-similar flows is explored. This analogy provides a simple steady-unsteady relationship. The criteria for the validity of the steady-unsteady analogy are also examined. Two different theoretical techniques are used to represent the separated shear layers based on the steady-unsteady analogy, neglecting the trailing edge effect. In the first approach, each vortex system is represented by a pair of concentrated vortices connected to the separation points by straight feeding sheets. In the second approach, the vortex cloud method is adopted for simulating the flow field in the crossflow plane. The separated shear layers are replaced with a cloud of discrete vortices and the boundary element method is employed to represent the wing trace by a vorticity distribution. A simple merging scheme is used to model the core region of the vortical flow as a single vortex by imposing a restriction on the shear layer rotation angle. The results are compared with experiments and with results from 3-D panel calculations.

Oh, S.↗

NASA NTRS2000

Hypersonic Boundary-Layer Trip Development for Hyper-X

Boundary layer trip devices for the Hper-X forebody have been experimentally examined in several wind tunnels. Five different trip configurations were compared in three hypersonic facilities, the LaRC 20-Inch Mach 6 Air Tunnel, the LaRC 31 -Inch Mach 10 Air Tunnel, and in the HYPULSE Reflected Shock Tunnel at GASL. Heat transfer distributions, utilizing the phosphor thermography and thin-film techniques, shock system details, and surface streamline patterns were measured on a 0.333-scale model of the Hyper-X forebody. Parametric variations include angles-of-attack of 0-deg, 2-deg, and 4-deg; Reynolds numbers based on model length of 1.2 to 15.4 million: and inlet cowl door simulated in both open and closed positions. Comparisons of transition due to discrete roughness elements have led to the selection of a trip configuration for the Hyper-X Mach 7 flight vehicle.

Berry, Scott A.↗

NASA NTRS2001

Visualization of CFD Results in Immersive Virtual Environments

An object-oriented event-driven immersive virtual environment (VE) is described for the visualization of computational fluid dynamics (CFD) results. The VE incorporates the following types of primitive software objects: interface objects, support objects, geometric entities, and finite elements. The fluid domain is discretized using either a multi-block structured grid or an unstructured finite element mesh. The VE allows natural 'fly-through' visualization of the model, the CFD grid, and the model's surroundings. In order to help visualize the flow and its effects on the model, the VE incorporates the following objects: stream objects (lines, surface-restricted lines. ribbons. and volumes); colored surfaces; elevation surfaces; surface arrows; global and local iso-surfaces; vortex cores; and separation/attachment surfaces and lines. Most of these objects can be used for dynamically probing the flow. Particles and arrow animations can be displayed on top of stream objects. Primitive response quantities as well as derived quantities can be used. A recursive tree search algorithm is used for real-time point and value search in the CFD grid.

Wasfy, Tamer M.↗

NASA NTRS1999

X-33 Hypersonic Boundary Layer Transition

Boundary layer and aeroheating characteristics of several X-33 configurations have been experimentally examined in the Langley 20-Inch Mach 6 Air Tunnel. Global surface heat transfer distributions, surface streamline patterns, and shock shapes were measured on 0.013-scale models at Mach 6 in air. Parametric variations include angles-of-attack of 20-deg, 30-deg, and 40-deg; Reynolds numbers based on model length of 0.9 to 6.6 million; and body-flap deflections of 0, 10 and 20-deg. The effects of discrete and distributed roughness elements on boundary layer transition, which included trip height, size, location, and distribution, both on and off the windward centerline, were investigated. The discrete roughness results on centerline were used to provide a transition correlation for the X-33 flight vehicle that was applicable across the range of reentry angles of attack. The attachment line discrete roughness results were shown to be consistent with the centerline results, as no increased sensitivity to roughness along the attachment line was identified. The effect of bowed panels was qualitatively shown to be less effective than the discrete trips; however, the distributed nature of the bowed panels affected a larger percent of the aft-body windward surface than a single discrete trip.

Berry, Scott A.↗

NASA NTRS2015

Incorporation of Plasticity and Damage Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. While there are several composite material models currently available within commercial transient dynamic finite element codes, several features have been identified as being lacking in the currently available material models that could substantially enhance the predictive capability of the impact simulations. A specific desired feature pertains to the incorporation of both plasticity and damage within the material model. Another desired feature relates to using experimentally based tabulated stress-strain input to define the evolution of plasticity and damage as opposed to specifying discrete input properties (such as modulus and strength) and employing analytical functions to track the response of the material. To begin to address these needs, a combined plasticity and damage model suitable for use with both solid and shell elements is being developed for implementation within the commercial code LS-DYNA. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. The effective plastic strain is computed by using the non-associative flow rule in combination with appropriate numerical methods. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used, in which a load in one direction results in a stiffness reduction in multiple coordinate directions. A specific laminated composite is examined to demonstrate the process of characterizing and analyzing the response of a composite using the developed model.

Impact↗

NASA NTRS2015

Incorporation of Plasticity and Damage Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

Impact↗

NASA NTRS1992

Stability of generally stiffened anisotropic noncircular cylinders

Continuous filament grid-stiffened structure is a stiffening concept that combines structural efficiency and damage tolerance. However, finite element design of such structures against buckling is expensive due to the complexities of the structure. An analytical model of such a structure is developed using a penalty method (artificial springs) with a first order shear deformation theory (FSDT). The buckling analysis under combined loadings is done using energy method with a penalty/Rayleigh-Ritz technique. The penalty/Rayleigh-Ritz approach is computationally less demanding when compared to the finite element solution and mesh generation. Apart from the published research works on buckling of stiffened plates and shells by finite element and finite strips, research works on buckling of stiffened plates and shells utilize three different approaches; smeared, column, and discrete approaches. The discrete approach considers the discrete effects of the stiffeners in the buckling behavior by modeling stiffeners as line of bending (EI) and torsion (GJ) stiffnesses on panel skin. Some local deformations are lost when stiffeners are modeled as (EI) and (GJ) stiffeners. This approach becomes difficult in the case of plate stiffened in more than two directions. Most of the work done using the discrete approach involved the Classical Plate Theory (CLPT) rather than the FSDT. We report on our formulation of a discrete approach coupled with a penalty formulation and FSDT.

Sobh, Nahil Atef↗

NASA NTRS2001

Mechanical behavior in living cells consistent with the tensegrity model

Alternative models of cell mechanics depict the living cell as a simple mechanical continuum, porous filament gel, tensed cortical membrane, or tensegrity network that maintains a stabilizing prestress through incorporation of discrete structural elements that bear compression. Real-time microscopic analysis of cells containing GFP-labeled microtubules and associated mitochondria revealed that living cells behave like discrete structures composed of an interconnected network of actin microfilaments and microtubules when mechanical stresses are applied to cell surface integrin receptors. Quantitation of cell tractional forces and cellular prestress by using traction force microscopy confirmed that microtubules bear compression and are responsible for a significant portion of the cytoskeletal prestress that determines cell shape stability under conditions in which myosin light chain phosphorylation and intracellular calcium remained unchanged. Quantitative measurements of both static and dynamic mechanical behaviors in cells also were consistent with specific a priori predictions of the tensegrity model. These findings suggest that tensegrity represents a unified model of cell mechanics that may help to explain how mechanical behaviors emerge through collective interactions among different cytoskeletal filaments and extracellular adhesions in living cells.

NASA Discipline Cell Biology↗

NASA NTRS1992

Thermal residual stresses in silicon-carbide/titanium (0/90) laminate

The current work formulated a micromechanical analysis of a cross-ply laminate and calculated the thermal residual stress in a very thick (0/90)(sub 2n) silicon-carbide/titanium laminate. Results were also shown for a unidirectional laminate of the same material. Discrete fiber-matrix models assuming a rectangular array of fibers with a fiber volume fraction of 32.5 percent and a three-dimensional, finite-element analysis were used. Significant differences in the trends and magnitudes for the fiber, matrix, and interface stresses were calculated for unidirectional and (0/90) models. Larger hoop stresses calculated for the (0/90) model indicate that it may be more susceptible to radial cracking when subjected to mechanical loading than the unidirectional model. The axial stresses in the matrix were calculated to be slightly larger for the (0/90) model. The compressive axial stresses in the fiber were significantly larger in the (0/90) model. The presence of the cross-ply in the (0/90) model reduced the constraint on the fiber, producing radial interface stresses that were less compressive, which could lead to earlier failure of the fiber-matrix interface.

Bigelow, C. A.↗