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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 NTRS1988

Probabilistic finite elements for fracture mechanics

The probabilistic finite element method (PFEM) is developed for probabilistic fracture mechanics (PFM). A finite element which has the near crack-tip singular strain embedded in the element is used. Probabilistic distributions, such as expectation, covariance and correlation stress intensity factors, are calculated for random load, random material and random crack length. The method is computationally quite efficient and can be expected to determine the probability of fracture or reliability.

Besterfield, Glen↗

NASA NTRS1990

Computing Deformations Of Rubbery Materials

Better use made of experimental data in finite-element computations. New formulation of constitutive equations of rubbery, nonlinearly elastic material enables finite-element analysis of boundary-value stress-and-strain problems involving arbitrary shapes and loads. In development of formulation, principal stretches used as arguments of strain-energy-density function.

Peng, Steven T. J.↗

NASA NTRS1989

Analytical and computational models of shells; Proceedings of the Symposium, ASME Winter Annual Meeting, San Francisco, CA, Dec. 10-15, 1989

Topics presented include asymptotic analysis and computation for shells, the edge effects in the Reissner-Mindlin plate theory, nonlinear problems of geometrically exact shell theories, and developments in variational methods for high performance plate and shell elements. Also presented are an assumed strain solid element model for geometrically nonlinear shell analysis, shell finite elements with six degrees of freedom per node, hierarchic plate and shell models based on p-extension, and a simple shell element formulation for large-scale elastoplastic analysis. Also discussed are the assessment of computational models for multilayered composite cylinders, shell models for impact analysis, analysis of shell structures subjected to contact-impacts, and the application of shell theory to cardiac mechanics.

Noor, Ahmed K.↗

NASA NTRS1990

Modal analysis of UH-60A instrumented rotor blades

The dynamic characteristics of instrumented and production UH-60A Black Hawk main rotor blades were measured, and the results were validated with NASTRAN finite element models. The blades tested included pressure and strain-gage instrumented blades, which are part of the NASA Airloads Flight Research Phase of the Modern Technology Rotor Program. The dynamic similarity of the blades was required for accurate data collection in this program. Therefore, a nonrotating blade modal analysis was performed on the first 10 free-free modes to measure blade similarities. The results showed small differences between the modal frequencies of instrumented and production blades and a close correlation with the NASTRAN models. This type of modal testing and analysis is recommended as a standard procedure for future instrumented blade flight testing.

Hamade, Karen S.↗

NASA NTRS1991

Damage prediction in cross-plied curved composite laminates

Analytical and experimental work is detailed which is required to predict delamination onset and growth in a curved cross plied composite laminate subjected to static and fatigue loads. The composite used was AS4/3501/6, graphite/epoxy. Analytically, a closed form stress analysis and 2-D and 3-D finite element analyses were conducted to determine the stress distribution in an undamaged curved laminate. The finite element analysis was also used to determine values of strain energy release rate at a delamination emanating from a matrix crack in a 90 deg ply. Experimentally, transverse tensile strength and fatigue life were determined from flat 90 deg coupons. The interlaminar tensile strength and fatigue life were determined from double cantilevered beam specimens. Cross plied curved laminates were tested statically and in fatigue to give a comparison to the analytical predictions. A comparison of the fracture mechanics life prediction technique and the strength based prediction technique is given.

Martin, Roderick H.↗

NASA NTRS1990

Modal analysis of UH 60A instrumented rotor blades

The dynamic characteristics of instrumented and production UH-60A Black Hawk main rotor blades were measured, and the results were validated with NASTRAN finite element models. The blades tested included pressure and strain-gage instrumented blades which are part of NASA's Airloads Flight Research Phase of the Modern Technology Rotor Program. The dynamic similarity of the blades was required for accurate data collection in this program. Therefore, a nonrotating blade modal analysis was performed on the first 10 free-free modes to measure blade similarities. The results showed small differences between the modal frequencies of instrumented and production blades and a close correlation with the NASTRAN models. This type of modal testing and analysis is recommended as a standard procedure for future instrumented blade flight testing.

Hamade, Karen S.↗

NASA NTRS1993

Brief summary of the evolution of high-temperature creep-fatigue life prediction models for crack initiation

The evolution of high-temperature, creep-fatigue, life-prediction methods used for cyclic crack initiation is traced from inception in the late 1940's. The methods reviewed are material models as opposed to structural life prediction models. Material life models are used by both structural durability analysts and by material scientists. The latter use micromechanistic models as guidance to improve a material's crack initiation resistance. Nearly one hundred approaches and their variations have been proposed to date. This proliferation poses a problem in deciding which method is most appropriate for a given application. Approaches were identified as being combinations of thirteen different classifications. This review is intended to aid both developers and users of high-temperature fatigue life prediction methods by providing a background from which choices can be made. The need for high-temperature, fatigue-life prediction methods followed immediately on the heels of the development of large, costly, high-technology industrial and aerospace equipment immediately following the second world war. Major advances were made in the design and manufacture of high-temperature, high-pressure boilers and steam turbines, nuclear reactors, high-temperature forming dies, high-performance poppet valves, aeronautical gas turbine engines, reusable rocket engines, etc. These advances could no longer be accomplished simply by trial and error using the 'build-em and bust-em' approach. Development lead times were too great and costs too prohibitive to retain such an approach. Analytic assessments of anticipated performance, cost, and durability were introduced to cut costs and shorten lead times. The analytic tools were quite primitive at first and out of necessity evolved in parallel with hardware development. After forty years more descriptive, more accurate, and more efficient analytic tools are being developed. These include thermal-structural finite element and boundary element analyses, advanced constitutive stress-strain-temperature-time relations, and creep-fatigue-environmental models for crack initiation and propagation. The high-temperature durability methods that have evolved for calculating high-temperature fatigue crack initiation lives of structural engineering materials are addressed. Only a few of the methods were refined to the point of being directly useable in design. Recently, two of the methods were transcribed into computer software for use with personal computers.

Halford, Gary R.↗

NASA NTRS1999

Determination of Creep Behavior of Thermal Barrier Coatings Under Laser Imposed High Thermal and Stress Gradient Conditions

A laser sintering/creep technique has been established to determine the creep behavior of thermal barrier coatings under steady-state high heat flux conditions. For a plasma sprayed zirconia-8 wt. % yttria coating, a significant primary creep strain and a low apparent creep activation energy were observed. Possible creep mechanisms involved include stress induced mechanical sliding and temperature and stress enhanced cation diffusion through the splat and grain boundaries. The elastic modulus evolution, stress response, and total accumulated creep strain variation across the ceramic coating are simulated using a finite difference approach. The modeled creep response is consistent with experimental observations.

Zhu, Dongming↗

NASA NTRS2002

Fatigue Life Analysis of Tapered Hybrid Composite Flexbeams

Nonlinear-tapered flexbeam laminates from a full-size composite helicopter rotor hub flexbeam were tested under combined constant axial tension and cyclic bending loads. The two different graphite/glass hybrid configurations tested under cyclic loading failed by delamination in the tapered region. A 2-D finite element model was developed which closely approximated the flexbeam geometry, boundary conditions, and loading. The analysis results from two geometrically nonlinear finite element codes, ANSYS and ABAQUS, are presented and compared. Strain energy release rates (G) obtained from the above codes using the virtual crack closure technique (VCCT) at a resin crack location in the flexbeams are presented for both hybrid material types. These results compare well with each other and suggest that the initial delamination growth from the resin crack toward the thick region of the flexbeam is strongly mode II. The peak calculated G values were used with material characterization data to calculate fatigue life curves and compared with test data. A curve relating maximum surface strain to number of loading cycles at delamination onset compared reasonably well with the test results.

Murri, Gretchen B.↗

NASA NTRS2003

High-Fidelity Micromechanics Model Enhanced for Multiphase Particulate Materials

This 3-year effort involves the development of a comprehensive micromechanics model and a related computer code, capable of accurately estimating both the average response and the local stress and strain fields in the individual phases, assuming both elastic and inelastic behavior. During the first year (fiscal year 2001) of the investigation, a version of the model called the High-Fidelity Generalized Method of Cells (HFGMC) was successfully completed for the thermo-inelastic response of continuously reinforced multiphased materials with arbitrary periodic microstructures (refs. 1 and 2). The model s excellent predictive capability for both the macroscopic response and the microlevel stress and strain fields was demonstrated through comparison with exact analytical and finite element solutions. This year, HFGMC was further extended in two technologically significant ways. The first enhancement entailed the incorporation of fiber/matrix debonding capability into the two-dimensional version of HFGMC for modeling the response of unidirectionally reinforced composites such as titanium matrix composites, which exhibit poor fiber/matrix bond. Comparison with experimental data validated the model s predictive capability. The second enhancement entailed further generalization of HFGMC to three dimensions to enable modeling the response of particulate-reinforced (discontinuous) composites in the elastic material behavior domain. Next year, the three-dimensional version will be generalized to encompass inelastic effects due to plasticity, viscoplasticity, and damage, as well as coupled electromagnetothermomechanical (including piezoelectric) effects.

Pindera, Marek-Jerzy↗

NASA NTRS2006

Fatigue Life Methodology for Tapered Hybrid Composite Flexbeams

Nonlinear-tapered flexbeam specimens from a full-size composite helicopter rotor hub flexbeam were tested under combined constant axial tension and cyclic bending loads. Two different graphite/glass hybrid configurations tested under cyclic loading failed by delamination in the tapered region. A 2-D finite element model was developed which closely approximated the flexbeam geometry, boundary conditions, and loading. The analysis results from two geometrically nonlinear finite element codes, ANSYS and ABAQUS, are presented and compared. Strain energy release rates (G) associated with simulated delamination growth in the flexbeams are presented from both codes. These results compare well with each other and suggest that the initial delamination growth from the tip of the ply-drop toward the thick region of the flexbeam is strongly mode II. The peak calculated G values were used with material characterization data to calculate fatigue life curves for comparison with test data. A curve relating maximum surface strain to number of loading cycles at delamination onset compared well with the test results.

urri, Gretchen B.↗

NASA NTRS2011

Extension of Ko Straight-Beam Displacement Theory to Deformed Shape Predictions of Slender Curved Structures

The Ko displacement theory originally developed for shape predictions of straight beams is extended to shape predictions of curved beams. The surface strains needed for shape predictions were analytically generated from finite-element nodal stress outputs. With the aid of finite-element displacement outputs, mathematical functional forms for curvature-effect correction terms are established and incorporated into straight-beam deflection equations for shape predictions of both cantilever and two-point supported curved beams. The newly established deflection equations for cantilever curved beams could provide quite accurate shape predictions for different cantilever curved beams, including the quarter-circle cantilever beam. Furthermore, the newly formulated deflection equations for two-point supported curved beams could provide accurate shape predictions for a range of two-point supported curved beams, including the full-circular ring. Accuracy of the newly developed curved-beam deflection equations is validated through shape prediction analysis of curved beams embedded in the windward shallow spherical shell of a generic crew exploration vehicle. A single-point collocation method for optimization of shape predictions is discussed in detail

Ko, William L.↗

NASA NTRS2016

Plasticity Tool for Predicting Shear Nonlinearity of Unidirectional Laminates Under Multiaxial Loading

This study implements a plasticity tool to predict the nonlinear shear behavior of unidirectional composite laminates under multiaxial loadings, with an intent to further develop the tool for use in composite progressive damage analysis. The steps for developing the plasticity tool include establishing a general quadratic yield function, deriving the incremental elasto-plastic stress-strain relations using the yield function with associated flow rule, and integrating the elasto-plastic stress-strain relations with a modified Euler method and a substepping scheme. Micromechanics analyses are performed to obtain normal and shear stress-strain curves that are used in determining the plasticity parameters of the yield function. By analyzing a micromechanics model, a virtual testing approach is used to replace costly experimental tests for obtaining stress-strain responses of composites under various loadings. The predicted elastic moduli and Poisson's ratios are in good agreement with experimental data. The substepping scheme for integrating the elasto-plastic stress-strain relations is suitable for working with displacement-based finite element codes. An illustration problem is solved to show that the plasticity tool can predict the nonlinear shear behavior for a unidirectional laminate subjected to multiaxial loadings.

Wang, John T.↗

NASA NTRS2007

Mesh Deformation Based on Fully Stressed Design: The Method and Two-Dimensional Examples

Mesh deformation in response to redefined boundary geometry is a frequently encountered task in shape optimization and analysis of fluid-structure interaction. We propose a simple and concise method for deforming meshes defined with three-node triangular or four-node tetrahedral elements. The mesh deformation method is suitable for large boundary movement. The approach requires two consecutive linear elastic finite-element analyses of an isotropic continuum using a prescribed displacement at the mesh boundaries. The first analysis is performed with homogeneous elastic property and the second with inhomogeneous elastic property. The fully stressed design is employed with a vanishing Poisson s ratio and a proposed form of equivalent strain (modified Tresca equivalent strain) to calculate, from the strain result of the first analysis, the element-specific Young s modulus for the second analysis. The theoretical aspect of the proposed method, its convenient numerical implementation using a typical linear elastic finite-element code in conjunction with very minor extra coding for data processing, and results for examples of large deformation of two-dimensional meshes are presented in this paper. KEY WORDS: Mesh deformation, shape optimization, fluid-structure interaction, fully stressed design, finite-element analysis, linear elasticity, strain failure, equivalent strain, Tresca failure criterion

Hsu, Su-Yuen↗

NASA NTRS2008

Integrated Force Method for Indeterminate Structures

Two methods of solving indeterminate structural-mechanics problems have been developed as products of research on the theory of strain compatibility. In these methods, stresses are considered to be the primary unknowns (in contrast to strains and displacements being considered as the primary unknowns in some prior methods). One of these methods, denoted the integrated force method (IFM), makes it possible to compute stresses, strains, and displacements with high fidelity by use of modest finite-element models that entail relatively small amounts of computation. The other method, denoted the completed Beltrami Mitchell formulation (CBMF), enables direct determination of stresses in an elastic continuum with general boundary conditions, without the need to first calculate displacements as in traditional methods. The equilibrium equation, the compatibility condition, and the material law are the three fundamental concepts of the theory of structures. For almost 150 years, it has been commonly supposed that the theory is complete. However, until now, the understanding of the compatibility condition remained incomplete, and the compatibility condition was confused with the continuity condition. Furthermore, the compatibility condition as applied to structures in its previous incomplete form was inconsistent with the strain formulation in elasticity.

Hopkins, Dale 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 NTRS1978

Adaptive finite element analysis based on p-convergence

The results of numerical experiments are presented in which a posteriori estimators of error in strain energy were examined on the basis of a typical problem in linear elastic fracture mechanics. Two estimators were found to give close upper and lower bounds for the strain energy error. The potential significance of this is that the same estimators may provide a suitable basis for adaptive redistribution of the degrees of freedom in finite element models.

Szabo, B. A.↗