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At least 235 records · Page 13

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NASA NTRS1981

Finite element analysis of instability-related delamination growth

A parametric study of postbuckled through-width delaminations in laminated coupons was performed. A finite element analysis was developed to analyze the coupons as a combination of linear and geometrically nonlinear components. Because most of the coupon configuration studied behaves linearly, the mixed linear and nonlinear analysis greatly reduced computational costs. The analysis was verified by comparing numerical with exact solutions for simple hypothetical problems. In addition, measured lateral deflections of postbuckled through-width delaminations in laminated coupons were compared with predicted deflections. In the parametric study, stress distributions and strain-energy release rates were calculated for various delamination lengths, delamination depths, applied loads, and lateral deflections. Also, a small number of coupons with through-width delaminations were fatigue tested to obtain delamination growth data. Calculated strain-energy release rates were compared with the observed growth rates to determine the relative importance of the Mode 1 and Mode 2 components of energy release. Growth process was dominated by G sub I.

Whitcomb, J. D.↗

NASA NTRS1973

An improved numerical process for solution of solid mechanics problems

This paper gives an overview of the development and status of an improved numerical process for the solution of solid mechanics problems. The proposed process uses a mixed formulation with the fundamental unknowns consisting of both stress and displacement parameters. The problem is formulated either by means of first-order partial differential equations or in a variational form by using a Hellinger-Reissner-type mixed variational principle. For presentation purposes, the components of a numerical process are characterized and the criteria for an ideal process are outlined. Commonly used finite-difference and finite-element procedures are examined in the light of these criteria and it is shown that they fall short in a number of ways. The proposed numerical process, on the other hand, satisfies most of the optimality criteria and appears to be particularly suited for use with the forthcoming generation computers.

Noor, A. K.↗

NASA NTRS1984

Application of Iosipescu specimen geometry to determination of shear strength in unidirectional composites

The Iosipescu (1967) test method, in conjunction with a finite element analysis of anisotropic, unidirectionally reinforced composite specimens, can be used to derive composite shear strength values despite the small size of the samples used. When such a specimen is loaded parallel to the fiber direction, fracture occurs by shear within a narrow region near the center of the specimen; this is consistent with the maximum shear area determined by finite element analysis. The resulting fracture surface, as observed, is characteristic of shear failure, occurring either within the matrix or at the fiber-matrix interface. Problems of compressive and mixed mode failure which accrue to short beam shear specimens are by the present method precluded.

Hurwitz, F. I.↗

NASA NTRSDate not supplied

An Investigation on the Accuracy of Delamination Analysis Predictions for Unidirectional Laminate Configurations

The state-of-the-art methodologies for predicting delamination growth in composite laminates make use of the concept of mixed-mode fracture mechanics. In mixed-mode fracture approaches the individual Mode I, Mode II and Mode III components of the strain energy release rate (SERR) need to be determined under general loading conditions. Through the use of mixed-mode fracture, the individual components are used in combination with the critical strain energy release rates (interlaminar fracture toughnesses) for each fracture mode in a mixed mode criterion in order to predict delamination extension. These interlaminar fracture toughnesses are traditionally obtained by testing of unidirectional laminate coupons. This work presents an investigation on the accuracy of Double Cantilever Beam (DCB), End Notch Flexure (ENF) and Mixed-Mode Bending (MMB) delamination analysis predictions by comparing measured total strain-energy release rates obtained experimentally to results for structural analysis from closed-form expressions, shell finite element analysis, and continuum two-dimensional (2D) and three-dimensional (3D) (solid) finite element analysis.

Patrick Enjuto↗

NASA NTRS1988

Three-dimensional analysis of a postbuckled embedded delamination

Delamination growth caused by local buckling of a delaminated group of plies was investigated. Delamination growth was assumed to be governed by the strain energy release rates, G(1), G(2) and G(3). The strain energy release rates were calculated using a geometrically nonlinear three-dimensional finite element analysis. The program is described and several checks of the analysis are discussed. Based on a limited parametric study, the following conclusions were reached: (1) the problem is definitely mixed mode (in some cases G(1) is larger than G(2), for other cases the opposite is true); (2) in general, there is a large gradient in the strain energy release rates along the delamination front; (3) the locations of maximum G(1) and G(2) depend on the delamination shape and the applied strain; (4) the mode 3 component was negligible for all cases considered; and (5) the analysis predicted that parts of the delamination would overlap. The results presented did not impose contact constraints to prevent overlapping. Further work is needed to determine the effects of allowing the overlapping.

Whitcomb, John D.↗

NASA NTRS1989

Three-dimensional analysis of a postbuckled embedded delamination

Whitcomb, John D.↗

NASA NTRS2022

A Cohesive Element Formulation for Simulation of General Mode I, II and III Delamination

Cohesive element formulations proposed thus far have assumed that Mode II and Mode III fracture processes, and hence traction-separation laws, are identical. However, experimental observations suggest that such an assumption may not hold in general. The approach described herein consists of a cohesive element formulation in which the assumption of identical Mode II and Mode III fracture processes is not required. This assumption is alleviated by estimating the normal to the delamination front based on the gradient of the displacement jumps determined within each element. The estimated normal is used to rotate the cohesive element coordinate system. Determining the displacement jumps in the rotated coordinate system enables the distinction between Mode II sliding, and Mode III tearing. This information is subsequently used to extend a recently proposed cohesive formulation, resulting in an approach that can simulate mixed-mode I/II/III fracture via prescribing piecewise-linear traction-separation laws combined with a 3D mixed-mode fracture criteria.

Delamination↗

NASA NTRS1992

Mixed mode stress-intensity-factors in mode-3 loaded middle crack tension specimen

A three dimensional stress analysis of a middle-crack tension specimen subjected to mode-3 type loading was performed using fracture mechanics based finite element code FRAC3D. Three-dimensional stress intensity factors were calculated for a range of specimen thicknesses that represent the structures used in aerospace and nuclear industries. Calculated SIF for very thick specimen (thickness-to-crack length b/a greater than or equal to 30) agreed very well with the antiplane solution in the literature. The K(sub II) stress field exists near the intersection of the crack front and free surface in a boundary-layer region covers the complete thickness of the plate and K(sub II) dominates all through the thickness. For very thin plates (b/a is less than .1), the average K(sub II) is larger than K(sub III) (about 25% for b/a = 0.1).

Shivakumar, Kunigal N.↗

NASA NTRS1995

Finite element buckling and postbuckling solutions for multilayered composite panels

A study is made of the buckling and postbuckling responses of flat, unstiffened composite panels subjected to various combinations of mechanical and thermal loads. The analysis is based on a first-order shear deformation von Karman-type plate theory. A mixed formulation is used with the fundamental unknowns consisting of the strain components, stress resultants and the generalized displacements of the plate. The stability boundary, postbuckling response and the sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the buckling and postbuckling responses to variations in the different lamination and material parameters of the panel. Numerical results are presented for both solid panels and panels with central circular cutouts. The results show the effects of the variations in the fiber orientation angels, aspect ratio of the panel, and the hole diameter (for panels with cutouts) on the stability boundary, postbuckling response and sensitivity coefficients.

Noor, Ahmed K.↗

NASA NTRS1984

The solution of non-linear hyperbolic equation systems by the finite element method

A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.

Loehner, R.↗

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↗

NASA NTRS1987

A quadrilateral shell element using a mixed formulation

A simple quadrilateral shell element consisting of five nodes, four corner nodes and a central node, is developed for linear elastic analysis of thin as well as moderately thick shells. Based on a modified Hellinger-Reissner principle, finite element equations are derived from the assumed displacement and strain fields. By carefully choosing appropriate strain terms, all kinematic deformation modes are suppressed. Although the present element is similar to a displacement-based degenerated shell, no locking is experienced when it is applied to thin shell problems. Five examples are given to illustrate the analysis capability of the shell element. Numerical results indicate that the element shows fast mesh convergence and gives excellent stress predictions.

Saleeb, A. F.↗

NASA NTRS1979

The fracture criteria for crack growth under biaxial loading

The paper examines the fracture criteria for crack growth under biaxial loading. A finite element theory was formulated for the problem of crack propagation to failure which is based on the incremental theory of plasticity and is mathematically equivalent to that of a nonlinear moving-mixed-boundary-value problem. It was found that during the crack growth the plastic energy of the specimen and the crack size are linearly related for center-cracked specimens of an aluminum alloy subjected to uniaxial and or biaxial loading when experimental data relating applied stress and crack size have been used as input.

Liebowitz, H.↗

NASA NTRS1983

Finite element computational fluid mechanics

Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.

Baker, A. J.↗

NASA NTRS1998

Simulation of Conformal Spiral Slot Antennas on Composite Platforms

During the course of the grant, we wrote and distributed about 12 reports and an equal number of journal papers supported fully or in part by this grant. The list of reports (title & abstract) and papers are given in Appendices A and B. This grant has indeed been instrumental in developing a robust hybrid finite element method for the analysis of complex broadband antennas on doubly curved platforms. Previous to the grant, our capability was limited to simple printed patch antennas on mostly planar platforms. More specifically: (1) mixed element formulations were developed and new edge-based prisms were introduced; (2) these elements were important in permitting flexibility in geometry gridding for most antennas of interest; (3) new perfectly matched absorbers were introduced for mesh truncations associated with highly curved surfaces; (4) fast integral algorithms were introduced for boundary integral truncations reducing CPU time from O(N-2) down to O(N-1.5) or less; (5) frequency extrapolation schemes were developed for efficient broadband performance evaluations. This activity has been successfully continued by NASA researchers; (6) computer codes were developed and extensively tested for several broadband configurations. These include FEMA-CYL, FEMA-PRISM and FEMA-TETRA written by L. Kempel, T. Ozdemir and J. Gong, respectively; (7) a new infinite balun feed was designed nearly constant impedance over the 800-3000 MHz operational band; (8) a complete slot spiral antenna was developed, fabricated and tested at NASA Langley. This new design is a culmination of the projects goals and integrates the computational and experimental efforts. this antenna design resulted in a U.S. patent and was revised three times to achieve the desired bandwidth and gain requirements from 800-3000 MHz.

Volakis, J. L.↗

NASA NTRS1987

Petrov-Galerkin methods for natural convection in directional solidification of binary alloys

A Petrov-Galerkin finite element method is presented for calculation of the steady, axisymmetric thermosolutal convection and interface morphology in a model for vertical Bridgman crystal growth of nondilute binary alloys. The Petrov-Galerkin method is based on the formulation for biquadratic elements developed by Heinrich and Zienkiewicz and is introduced into the calculation of the velocity, temperature and concentration fields. The algebraic system is solved simultaneously for the field variables and interface shape by Newton's method. The results of the Petrov-Galerkin method are compared critically with those of Galerkin's method using the same finite element grids. Significant improvements in accuracy are found with the Petrov-Galerkin method only when the mesh is refined and when the formulation of the residual equations is modified to account for the mixed boundary conditions that arise at the solidification interface. Calculations for alloys with stable and unstable solute gradients show the occurrence of classical flow transitions and morphological instabilities in the solidification system.

Adornato, Peter M.↗

NASA NTRS2001

A Shell/3D Modeling Technique for the Analyses of Delaminated Composite Laminates

A shell/3D modeling technique was developed for which a local three-dimensional solid finite element model is used only in the immediate vicinity of the delamination front. The goal was to combine the accuracy of the full three-dimensional solution with the computational efficiency of a plate or shell finite element model. Multi-point constraints provided a kinematically compatible interface between the local three-dimensional model and the global structural model which has been meshed with plate or shell finite elements. Double Cantilever Beam (DCB), End Notched Flexure (ENF), and Single Leg Bending (SLB) specimens were modeled using the shell/3D technique to study the feasibility for pure mode I (DCB), mode II (ENF) and mixed mode I/II (SLB) cases. Mixed mode strain energy release rate distributions were computed across the width of the specimens using the virtual crack closure technique. Specimens with a unidirectional layup and with a multidirectional layup where the delamination is located between two non-zero degree plies were simulated. For a local three-dimensional model, extending to a minimum of about three specimen thicknesses on either side of the delamination front, the results were in good agreement with mixed mode strain energy release rates obtained from computations where the entire specimen had been modeled with solid elements. For large built-up composite structures modeled with plate elements, the shell/3D modeling technique offers a great potential for reducing the model size, since only a relatively small section in the vicinity of the delamination front needs to be modeled with solid elements.

Krueger, Ronald↗

NASA NTRS2016

Multiscale Static Analysis of Notched and Unnotched Laminates Using the Generalized Method of Cells

The generalized method of cells (GMC) is demonstrated to be a viable micromechanics tool for predicting the deformation and failure response of laminated composites, with and without notches, subjected to tensile and compressive static loading. Given the axial [0], transverse [90], and shear [+45/-45] response of a carbon/epoxy (IM7/977-3) system, the unnotched and notched behavior of three multidirectional layups (Layup 1: [0,45,90,-45](sub 2S), Layup 2: [0,60,0](sub 3S), and Layup 3: [30,60,90,-30, -60](sub 2S)) are predicted under both tensile and compressive static loading. Matrix nonlinearity is modeled in two ways. The first assumes all nonlinearity is due to anisotropic progressive damage of the matrix only, which is modeled, using the multiaxial mixed-mode continuum damage model (MMCDM) within GMC. The second utilizes matrix plasticity coupled with brittle final failure based on the maximum principle strain criteria to account for matrix nonlinearity and failure within the Finite Element Analysis--Micromechanics Analysis Code (FEAMAC) software multiscale framework. Both MMCDM and plasticity models incorporate brittle strain- and stress-based failure criteria for the fiber. Upon satisfaction of these criteria, the fiber properties are immediately reduced to a nominal value. The constitutive response for each constituent (fiber and matrix) is characterized using a combination of vendor data and the axial, transverse, and shear responses of unnotched laminates. Then, the capability of the multiscale methodology is assessed by performing blind predictions of the mentioned notched and unnotched composite laminates response under tensile and compressive loading. Tabulated data along with the detailed results (i.e., stress-strain curves as well as damage evolution states at various ratios of strain to failure) for all laminates are presented.

GMC↗