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NASA NTRS1989

Sublaminate analysis of interlaminar fracture in composites. I - Analytical model

A simple analysis method based on a transverse shear-deformation theory and a sublaminate approach is utilized to analyze a mixed-mode edge delamination specimen. The analysis provides closed-form expressions for the interlaminar shear stresses ahead of the crack, the total strain-energy release rate, and the strain-energy release-rate components. The parameters controlling the behavior are identified. The effect of specimen stacking sequence and delamination interface on the strain energy release rate components is investigated. Results are compared with a finite-element simulation for reference. The simple nature of the method makes it suitable for preliminary design analyses which require a large number of configurations to be evaluated quickly and economically.

Armanios, Erian A.↗

DOE OSTI2022

Thermal conductivity of crack-containing media: A numerical study

The present study aims to evaluate the effective thermal conduction behavior of crack-containing media through micromechanical modeling. Numerical analyses were performed using the finite element method, first using periodic arrays of elliptical pores and then reducing the elliptical minor axis to reach the crack limit. This parametric approach was seen to be able to capture the effect of discontinuity across the crack face in a straightforward manner. The overall thermal conductivity of the model structures, encompassing a range of crack densities and spatial distributions, was investigated. It was found that, for cracks with mixed orientations, the effective thermal conductivity is insensitive to the actual crack alignment and can be uniquely represented by the crack density. The mixed-orientation periodic crack configurations are also representative of random sizes, orientations, and spatial distributions of cracks, thus exhibiting a high degree of generality. The modeling analyses can also be used to determine simple empirical expressions for two- and three-dimensional media containing random cracks.

36 MATERIALS SCIENCE↗

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 NTRS1989

Treatment of coupled fluid-structure interaction problems by a mixed variational principle

A general three-field variational principle is obtained for the motion of an acoustic fluid enclosed in a rigid or flexible container by the method of canonical decomposition applied to a modified form of the wave equation in the displacement potential. The general principle is specialized to a mixed two-field principle that contains the fluid displacement potential and pressure as independent fields. Semidiscrete finite-element equations of motion based on this principle are displayed.

Felippa, Carlos A.↗

NASA NTRSDate not supplied

F-ANG+: A 3-D Augmented-Stencil Face-Averaged Nodal-Gradient Cell-Centered Finite-Volume Method for Hypersonic Flows

We describe the extension of a 2-D simplified face-averaged nodal-gradient (F-ANG) method to 3-D and demonstrate that the 3-D simplified F-ANG method is accomplished by augmenting the nodecentered gradient least squares stencil. This augmented stencil F-ANG method is shown to result in advection and diffusion schemes that are stable for hexahedral, prismatic, pyramidal and tetrahedral cells without having to resort to cell-averaged nodal gradients. In addition, we describe the modifications to the augmented stencil required to support the use of wall function boundary conditions. Finally we describe a consistent, face-stencil based multi-dimensional limiter procedure (MLP), and show it to be fully consistent and compatible with the linearity-preserving unstructured- MUSCL (LP-U-MUSCL) scheme for all values of kappa. These methods and schema are implemented in the cell-centered finite-volume code VULCAN-CFD, which is then used to investigate whether the robustness improvements demonstrated in 2-D carry over to 3-D by computing hypersonic flows using mixed-element grids as well as highly adapted tetrahedral grids.

Weighted Least-Squares↗

DOE OSTI2025

On optimal control of hybrid dynamical systems using complementarity constraints

Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate them using non-smooth and non-convex complementarity constraints as a mathematical program with complementarity constraints (MPCC). We utilize a moving finite element based strategy to discretize the differential equation system to accurately locate the unknown switching points at the finite element boundary and achieve high-order accuracy at intermediate non-collocation points. We propose a globalization approach to solve the discretized MPCC problem using a mixed NLP/MILP-based strategy to converge to a non-spurious first-order optimal solution. The method is tested on three dynamic optimization examples, including a gas–liquid tank model and an optimal control problem with a sliding mode solution.

97 MATHEMATICS AND COMPUTING↗

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 NTRS1993

High Temperature Composite Analyzer (HITCAN) theoretical manual, version 1.0

This manual outlines some of the theoretical aspects embedded in the computer code, HITCAN (High Temperature Composite ANalyzer). HITCAN is a general purpose computer program for predicting nonlinear global structural and local stress-strain response of arbitrarily oriented, multilayered high temperature metal matrix composite structures. This code combines composite mechanics and laminate theory with an internal data base of the constituents (matrix, fiber and interface) material properties. The thermal and mechanical properties of the constituents are considered to be nonlinearly dependent on several parameters including temperature, stress and stress rate. The computational procedure for the analysis of the composite structure uses the finite element method. HITCAN consists of three modules: COBSTRAN, METCAN and MHOST. COBSTRAN generates the geometry (pre-processor) and defines the layup of the different plies. METCAN computes the material behavior of the composite and of the constituents. Finally, MHOST is a finite element program based on the mixed iterative solution technique. MHOST has a library for 2D and 3D isoparametric elements. HITCAN is written in FORTRAN 77 computer language and has been configured and executed on the NASA Lewis Research Center CRAY XMP and YMP computers.

Lackney, J. J.↗

NASA NTRS1999

Experimentally Determined Crack Location and Mixed Mode Stress Intensity Factors

This presentation first examines five strain field equations: the two modes of the Westergaard equations, and a mixed mode; the generalized coordinate system, and the significance testing of coefficients. It also discusses the weighted multiple linear least squares method, which shows why it is difficult to find the crack tip. The presentation then discusses the experiments to examine stress intensity. Lastly, comparison of finite element method results and experimental results is reviewed.

Zachary, Loren W.↗

NASA NTRS1995

Sensitivity analysis for the dynamic response of viscoplastic shells of revolution

A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic axisymmetric response of viscoplastic shells of revolution. The analytical formulation is based on Reissner's large deformation shell theory with the effects of transverse shear deformation, rotatory inertia and moments turning around the normal to the middle surface included. The material model is chosen to be isothermal viscoplasticity, and an associated flow rule is used with a von Mises effective stress. A mixed formulation is used with the fundamental unknowns consisting of six stress resultants, three generalized displacements and three velocity components. Spatial discretization is performed using finite elements, with discontinuous stress resultants across element interfaces. The temporal integration is performed by using an explicit central difference scheme (leap-frog method) with an implicit constitutive update. The sensitivity coefficients are evaluated using a direct differentiation approach. Numerical results are presented for a spherical cap subjected to step loading, and a circular plate subjected to impulsive loading. The sensitivity coefficients are generated by evaluating the derivatives of the response quantities with respect to thickness, mass density, Young's modulus, and two of the material parameters characterizing the viscoplastic response. Time histories of the response and sensitivity coefficients are presented, along with spatial distributions of these quantities at selected times.

Kulkarni, Makarand↗

NASA NTRS1993

Solution of mixed convection heat transfer from isothermal in-line fins

Transient and steady state combined natural and forced convective flows over two in-line finite thickness fins (louvers) in a vertical channel are numerically solved using two methods. The first method of solution is based on the 'Simple Arbitrary Lagrangian Eulerian' (SALE) technique which incorporates mainly two computational phases: (1) a Lagrangian phase in which the velocity field is updated by the effects of all forces, and (2) an Eulerian phase that executes all advective fluxes of mass, momentum and energy. The second method of solution uses the finite element code entitled FIDAP. In the first part, comparison of the results by FIDAP, SALE, and available experimental work were done and discussed for steady state forced convection over louvered fins. Good agreements were deduced between the three sets of results especially for the flow over a single fin. In the second part and in the absence of experimental literature, the numerical predictions were extended to the transient transports and to the opposing flow where pressure drop is reversed. Results are presented and discussed for heat transfer and pressure drop in assisting and opposing mixed convection flows.

Khalilollahi, Amir↗

NASA NTRS2008

Accuracy of Gradient Reconstruction on Grids with High Aspect Ratio

Gradient approximation methods commonly used in unstructured-grid finite-volume schemes intended for solutions of high Reynolds number flow equations are studied comprehensively. The accuracy of gradients within cells and within faces is evaluated systematically for both node-centered and cell-centered formulations. Computational and analytical evaluations are made on a series of high-aspect-ratio grids with different primal elements, including quadrilateral, triangular, and mixed element grids, with and without random perturbations to the mesh. Both rectangular and cylindrical geometries are considered; the latter serves to study the effects of geometric curvature. The study shows that the accuracy of gradient reconstruction on high-aspect-ratio grids is determined by a combination of the grid and the solution. The contributors to the error are identified and approaches to reduce errors are given, including the addition of higher-order terms in the direction of larger mesh spacing. A parameter GAMMA characterizing accuracy on curved high-aspect-ratio grids is discussed and an approximate-mapped-least-square method using a commonly-available distance function is presented; the method provides accurate gradient reconstruction on general grids. The study is intended to be a reference guide accompanying the construction of accurate and efficient methods for high Reynolds number applications

Thomas, James↗

NASA NTRS1979

Interlaminar crack growth in fiber reinforced composites during fatigue

This paper presents an investigation of interlaminar crack growth behavior in fiber-reinforced composites subjected to fatigue loading. In the experimental phase of the study, interlaminar crack propagation rates and mechanisms were determined for the cases of various geometries, laminate parameters and cyclic stress levels. An advanced singular hybrid-stress finite element method was used in conjunction with the experimental results to examine the local crack-tip behavior and to characterize the crack propagation during fatigue. Results elucidate the basic nature of the cyclic delamination damage and relate the interlaminar crack growth rate to the range of mixed-mode crack-tip stress intensity factors. The study provides fundamental insight into the problem, reveals several important features of the interlaminar fatigue failure, and should be of practical importance in selection, testing and design of composite materials.

Wang, S. S.↗

NASA NTRS1981

Interlaminar crack growth in fiber reinforced composites during fatigue, part 3

Interlaminar crack growth behavior in fiber-reinforced composites subjected to fatigue loading was investigated experimentally and theoretically. In the experimental phase, inter-laminar crack propagation rates and mechanisms were determined for the cases of various geometries, laminate parameters and cyclic stress levels. A singular hybrid-stress finite element method was used in conjuction with the experimental results to examine the local crack-tip behavior and to characterize the crack propagation during fatigue. Results elucidate the basic nature of the cyclic delamination damage, and relate the interlaminar crack growth rate to the range of mixed-mode crack-tip stress intensity factors. The results show that crack growth rates are directly related to the range of the mixed-mode cyclic stress intensity factors by a power law relationship.

Wang, S. S.↗

NASA NTRS1988

Computational simulation methods for composite fracture mechanics

Structural integrity, durability, and damage tolerance of advanced composites are assessed by studying damage initiation at various scales (micro, macro, and global) and accumulation and growth leading to global failure, quantitatively and qualitatively. In addition, various fracture toughness parameters associated with a typical damage and its growth must be determined. Computational structural analysis codes to aid the composite design engineer in performing these tasks were developed. CODSTRAN (COmposite Durability STRuctural ANalysis) is used to qualitatively and quantitatively assess the progressive damage occurring in composite structures due to mechanical and environmental loads. Next, methods are covered that are currently being developed and used at Lewis to predict interlaminar fracture toughness and related parameters of fiber composites given a prescribed damage. The general purpose finite element code MSC/NASTRAN was used to simulate the interlaminar fracture and the associated individual as well as mixed-mode strain energy release rates in fiber composites.

Murthy, Pappu L. N.↗

NASA NTRS1987

Shock structure in jets of arbitrary exit geometry

The shock structure and hydrodynamic stability of single and twin jets with arbitrary exit geometry are studied. Both vortex sheets and realistic mean profiles are considered for the jet shear layer. The boundary element method is used to predict the shock spacing and screech tones in a vortex sheet model of a single jet. Results are given for circular, elliptic and rectangular jets and the results compared with analysis and experiment. A finite difference technique is used to examine the effect of finite mixing layer thickness for a single jet. The hydrodynamic stability of twin circular jets is also considered. The variation of the stability characteristics are presented for the vortex sheet case for several separation distances. The formulation of the problem to account for finite thickness effects is also given.

Morris, P. J.↗

NASA NTRS1988

Composite interlaminar fracture toughness - Three-dimensional finite-element modeling for mixed mode I, II, and fracture

A computational method/procedure is described which can be used to simulate individual and mixed mode interlaminar fracture progression in fiber composite laminates. Different combinations of Modes 1, 2, and 3 fracture are simulated by varying the crack location through the specimen thickness and by selecting appropriate unsymmetric laminate configurations. The contribution of each fracture mode to strain energy release rate is determined by the local crack closure methods while the mixed mode is determined by global variables. The strain energy release rates are plotted versus extending crack length, where slow crack growth, stable crack growth, and rapid crack growth regions are easily identified. Graphical results are presented to illustrate the effectiveness and versatility of the computational simulation for: (1) evaluating mixed-mode interlaminar fracture, (2) for identifying respective dominant parameters, and (3) for selecting possible simple test methods.

Murthy, Pappu L. N.↗

NASA NTRS1986

Composite interlaminar fracture toughness: Three-dimensional finite element modeling for mixed mode 1, 2 and 3 fracture

Murthy, P. L. N.↗