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NASA NTRS2001

Decohesion Elements using Two and Three-Parameter Mixed-Mode Criteria

An eight-node decohesion element implementing different criteria to predict delamination growth under mixed-mode loading is proposed. The element is used at the interface between solid finite elements to model the initiation and propagation of delamination. A single displacement-based damage parameter is used in a softening law to track the damage state of the interface. The power law criterion and a three-parameter mixed-mode criterion are used to predict delamination growth. The accuracy of the predictions is evaluated in single mode delamination and in the mixed-mode bending tests.

Davila, Carlos G.↗

NASA NTRS1980

Application of a Galerkin finite element method to atmospheric transport problems

Numerical simulation of the movement of a contaminant within the atmosphere presents difficulties due to the multidimensionality of the problem and the fact that the horizontal transport is usually convection dominated, that the boundary conditions are mixed, and that both slow and fast atmospheric chemical reactions can be important. In this study, numerical experiments using a Crank-Nicolson Galerkin finite element method to solve the time-dependent partial differential equations demonstrate the applicability and accuracy of this method for the variety of conditions encountered in atmospheric pollutant modeling. The Crank-Nicolson Galerkin method using piecewise linear, piecewise cubic Hermite polynomials, and upwind finite elements is shown to accurately model the pure convection of initial wave forms. Numerical results studying the interactions of convection, diffusion, chemical reaction, pollutant removal, and the effects of contaminant emission source strength, source location and multiple sources are also presented.

Carmichael, G. R.↗

NASA NTRS1983

Performance of a quantitative study of instability-related delamination growth

An experimental program was conducted to quantify instability-induced imbedded delamination growth. Static tests on double cantilever beam (DCB) specimens yielded the critical mode 1 strain energy release rate (G sub 1 C) for T300/5208 graphite/epoxy. Static tests on mixed mode cracked lap shear (CLS) specimens, and a nonlinear finite element analysis (NFEA) of the CLS specimen to separate mode 1 and mode 2 effects, yielded the critical mode 2 strain energy release rate (G sub 2 C) for T300/5208. Constant amplitude fatigue tests on DCB and CLS specimens, along with the NFEA results on CLS specimens, quantified mode 1 and mode 2 contributions to delamination growth rate. Fatigue tests were conducted at a frequency (omega) of 10 Hertz, maintaining the minimum to maximum cyclic load ratio (R) at 0.05. Static compression and constant amplitude compression fatigue tests were also conducted on specimens with imbedded through the width (ITTW) delaminations. Kapton imbeddments were located below 3, 4 or 6 plies in a 64-ply laminate, during layup, to simulate ITTW delaminations.

Ramkumar, R. L.↗

NASA NTRS1984

Augmented weak forms and element-by-element preconditioners: Efficient iterative strategies for structural finite elements. A preliminary study

A weak formulation in structural analysis that provides well conditioned matrices suitable for iterative solutions is presented. A mixed formulation ensures the proper representation of the problem and the constitutive relations are added in a penalized form. The problem is solved by a double conjugate gradient algorithm combined with an element by element approximate factorization procedure. The double conjugate gradient strategy resembles Uzawa's variable-length type algorithms the main difference is the presence of quadratic terms in the mixed variables. In the case of shear deformable beams these terms ensure that the proper finite thickness solution is obtained.

Muller, A.↗

NASA NTRS1989

A simplified approach to strain energy release rate computations for interlaminar fracture of composites

A simple approach for the strain energy release rate computations based on the finite element method and a singular fitting model is presented. The model uses the stress and displacement distributions at the delamination front. The method is applied to a mixed-mode double cracked-lap-shear composite configuration. The strain energy release rate components predicted by the model are compared with the finite element crack-closure method. The effect of the mesh size on the stress and displacement distribution is isolated. The strain energy release rates predicted by relatively coarse mesh sizes are in good agreement with the finite element crack closure method.

Armanios, Erian A.↗

NASA NTRS1990

Edge delamination of composite laminates subject to combined tension and torsional loading

Delamination is a common failure mode of laminated composite materials. Edge delamination is important since it results in reduced stiffness and strength of the laminate. The tension/torsion load condition is of particular significance to the structural integrity of composite helicopter rotor systems. Material coupons can easily be tested under this type of loading in servo-hydraulic tension/torsion test stands using techniques very similar to those used for the Edge Delamination Tensile Test (EDT) delamination specimen. Edge delamination of specimens loaded in tension was successfully analyzed by several investigators using both classical laminate theory and quasi-three dimensional (Q3D) finite element techniques. The former analysis technique can be used to predict the total strain energy release rate, while the latter technique enables the calculation of the mixed-mode strain energy release rates. The Q3D analysis is very efficient since it produces a three-dimensional solution to a two-dimensional domain. A computer program was developed which generates PATRAN commands to generate the finite element model. PATRAN is a pre- and post-processor which is commonly used with a variety of finite element programs such as MCS/NASTRAN. The program creates a sufficiently dense mesh at the delamination crack tips to support a mixed-mode fracture mechanics analysis. The program creates a coarse mesh in those regions where the gradients in the stress field are low (away from the delamination regions). A transition mesh is defined between these regions. This program is capable of generating a mesh for an arbitrarily oriented matrix crack. This program significantly reduces the modeling time required to generate these finite element meshes, thus providing a realistic tool with which to investigate the tension torsion problem.

Hooper, Steven J.↗

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 NTRS1972

A theoretical study of mixing downstream of transverse injection into a supersonic boundary layer

A theoretical and analytical study was made of mixing downstream of transverse hydrogen injection, from single and multiple orifices, into a Mach 4 air boundary layer over a flat plate. Numerical solutions to the governing three-dimensional, elliptic boundary layer equations were obtained using a general purpose computer program. Founded upon a finite element solution algorithm. A prototype three-dimensional turbulent transport model was developed using mixing length theory in the wall region and the mass defect concept in the outer region. Excellent agreement between the computed flow field and experimental data for a jet/freestream dynamic pressure ratio of unity was obtained in the centerplane region of the single-jet configuration. Poorer agreement off centerplane suggests an inadequacy of the extrapolated two-dimensional turbulence model. Considerable improvement in off-centerplane computational agreement occured for a multi-jet configuration, using the same turbulent transport model.

Baker, A. J.↗

NASA NTRS1979

Delamination crack growth in unidirectional fiber-reinforced composites under static and cyclic loading

An investigation of delamination crack growth in a unidirectional composite laminate under static and fatigue loading conditions is presented. An experimental program was conducted to study failure mechanisms and characterize the crack growth rate; analytical modeling based on microscopic observations was carried out using an advanced singular finite element method of the hybrid-stress model. Using a mixed-mode failure criterion, the delamination growth under a monotonically increasing load can be predicted; the rate of delamination crack propagation under fatigue loading is directly related to the amplitudes of cyclic opening and shearing mode stress intensity factors by a power law relationship.

Wang, S. S.↗

NASA NTRSDate not supplied

Validation of Delamination Growth Predictions under Fatigue Loading using the Single Leg Bending Specimen

The Single Leg Bending Specimen (SLB) was chosen for a study to compare experimentally determined delamination growth with analysis predictions. First, fatigue tests were performed on SLB specimens with several different starter delamination lengths. Specimens were cycled in load control and delamination length increase was continuously recorded with increasing number of cycles. Test results from different load levels were combined to capture the entire delamination growth law (Paris Law) over a wide range of energy release rates. Second, a recently developed interpolation scheme was used to predict the Paris Law associated with the SLB specimen. This interpolation scheme allows the calculation of the growth rates for a given mixed-mode ratio from known single-mode growth laws. Third, finite element analyses were performed using two-dimensional models of the SLB specimen. New Virtual Crack Closure Technique based analysis tools for automated delamination growth analysis under cyclic loading in Abaqus were used for growth predictions. Fourth, the predictions from analyses were compared to experimental fatigue data. Remaining analysis shortcomings were highlighted.

Ronald Krueger↗

NASA NTRS1991

An equivalent domain integral method for three-dimensional mixed-mode fracture problems

A general formulation of the equivalent domain integral (EDI) method for mixed mode fracture problems in cracked solids is presented. The method is discussed in the context of a 3-D finite element analysis. The J integral consists of two parts: the volume integral of the crack front potential over a torus enclosing the crack front and the crack surface integral due to the crack front potential plus the crack face loading. In mixed mode crack problems the total J integral is split into J sub I, J sub II, and J sub III representing the severity of the crack front in three modes of deformations. The direct and decomposition methods are used to separate the modes. These two methods were applied to several mixed mode fracture problems, were analyzed, and results were found to agree well with those available in the literature. The method lends itself to be used as a post-processing subroutine in a general purpose finite element program.

Shivakumar, K. N.↗

NASA NTRS1992

An equivalent domain integral method for three-dimensional mixed-mode fracture problems

Shivakumar, K. N.↗

NASA NTRS2000

Curved Thermopiezoelectric Shell Structures Modeled by Finite Element Analysis

"Smart" structures composed of piezoelectric materials may significantly improve the performance of aeropropulsion systems through a variety of vibration, noise, and shape-control applications. The development of analytical models for piezoelectric smart structures is an ongoing, in-house activity at the NASA Glenn Research Center at Lewis Field focused toward the experimental characterization of these materials. Research efforts have been directed toward developing analytical models that account for the coupled mechanical, electrical, and thermal response of piezoelectric composite materials. Current work revolves around implementing thermal effects into a curvilinear-shell finite element code. This enhances capabilities to analyze curved structures and to account for coupling effects arising from thermal effects and the curved geometry. The current analytical model implements a unique mixed multi-field laminate theory to improve computational efficiency without sacrificing accuracy. The mechanics can model both the sensory and active behavior of piezoelectric composite shell structures. Finite element equations are being implemented for an eight-node curvilinear shell element, and numerical studies are being conducted to demonstrate capabilities to model the response of curved piezoelectric composite structures (see the figure).

Lee, Ho-Jun↗

NASA NTRS1988

MHOST: An efficient finite element program for inelastic analysis of solids and structures

An efficient finite element program for 3-D inelastic analysis of gas turbine hot section components was constructed and validated. A novel mixed iterative solution strategy is derived from the augmented Hu-Washizu variational principle in order to nodally interpolate coordinates, displacements, deformation, strains, stresses and material properties. A series of increasingly sophisticated material models incorporated in MHOST include elasticity, secant plasticity, infinitesimal and finite deformation plasticity, creep and unified viscoplastic constitutive model proposed by Walker. A library of high performance elements is built into this computer program utilizing the concepts of selective reduced integrations and independent strain interpolations. A family of efficient solution algorithms is implemented in MHOST for linear and nonlinear equation solution including the classical Newton-Raphson, modified, quasi and secant Newton methods with optional line search and the conjugate gradient method.

Nakazawa, S.↗

NASA NTRS1994

Axial crack propagation and arrest in pressurized fuselage

The crack arrest capability of a tear strap in a pressurized precracked fuselage was studied through instrumented axial rupture tests of small scale models of an idealized fuselage. Upon pressurization, rapid crack propagation initiated at an axial through crack along the stringer and immediately kinked due to the mixed modes 1 and 2 state caused by the one-sided opening of the crack flap. The diagonally running crack further turned at the tear straps. Dynamic finite element analysis of the rupturing cylinder showed that the crack kinked and also ran straight in the presence of a mixed mode state according to a modified two-parameter crack kinking criterion.

Kosai, M.↗

NASA NTRS2011

Seal Joint Analysis and Design for the Ares-I Upper Stage LOX Tank

The sealing capability of the Ares-I Upper Stage liquid oxygen tank-to-sump joint is assessed by analyzing the deflections of the joint components. Analyses are performed using three-dimensional symmetric wedge finite element models and the ABAQUS commercial finite element software. For the pressure loads and feedline interface loads, the analyses employ a mixed factor of safety approach to comply with the Constellation Program factor of safety requirements. Naflex pressure-assisted seals are considered first because they have been used successfully in similar seal joints in the Space Shuttle External Tank. For the baseline sump seal joint configuration with a Naflex seal, the predicted joint opening greatly exceeds the seal design specification. Three redesign options of the joint that maintain the use of a Naflex seal are studied. The joint openings for the redesigned seal joints show improvement over the baseline configuration; however, these joint openings still exceed the seal design specification. RACO pressure-assisted seals are considered next because they are known to also be used on the Space Shuttle External Tank, and the joint opening allowable is much larger than the specification for the Naflex seals. The finite element models for the RACO seal analyses are created by modifying the models that were used for the Naflex seal analyses. The analyses show that the RACO seal may provide sufficient sealing capability for the sump seal joint. The results provide reasonable data to recommend the design change and plan a testing program to determine the capability of RACO seals in the Ares-I Upper Stage liquid oxygen tank sump seal joint.

Phillips, Dawn R.↗

NASA NTRS1991

The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 1: Theoretical manual

Formulations and algorithms implemented in the MHOST finite element program are discussed. The code uses a novel concept of the mixed iterative solution technique for the efficient 3-D computations of turbine engine hot section components. The general framework of variational formulation and solution algorithms are discussed which were derived from the mixed three field Hu-Washizu principle. This formulation enables the use of nodal interpolation for coordinates, displacements, strains, and stresses. Algorithmic description of the mixed iterative method includes variations for the quasi static, transient dynamic and buckling analyses. The global-local analysis procedure referred to as the subelement refinement is developed in the framework of the mixed iterative solution, of which the detail is presented. The numerically integrated isoparametric elements implemented in the framework is discussed. Methods to filter certain parts of strain and project the element discontinuous quantities to the nodes are developed for a family of linear elements. Integration algorithms are described for linear and nonlinear equations included in MHOST program.

Nakazawa, Shohei↗

NASA NTRS1989

A least-squares finite element method for incompressible Navier-Stokes problem

Most finite element schemes for solving the Navier-Stokes equations can be categorized into the Galerkin mixed method and the penalty method. The mixed method leads to a saddle-point problem. In order to guarantee the existence of a solution, the combination of velocity and pressure interpolations requires satisfaction of the Ladyzhenskaya Babuska Brezzi (LBB) consistency condition which precludes the use of equal order interpolations and many seemingly natural pairs of velocity and pressure elements. In a previous paper a least-squares finite element method based on the first order velocity-pressure-vorticity formulation for the Stokes problem was proposed. This method leads to a minimization problem. The choice of combination of elements is thus not subject to the LBB condition. The numerical experiments exhibit the optimal rate of convergence for all variables with equal order interpolations. A theoretical error analysis supports the numerical results. In this paper the least-squares finite element method is extended to solving the incompressible Navier-Stokes problem.

Jiang, Bonan↗