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NASA NTRS1993

Nonlinear probabilistic finite element models of laminated composite shells

A probabilistic finite element analysis procedure for laminated composite shells has been developed. A total Lagrangian finite element formulation, employing a degenerated 3-D laminated composite shell with the full Green-Lagrange strains and first-order shear deformable kinematics, forms the modeling foundation. The first-order second-moment technique for probabilistic finite element analysis of random fields is employed and results are presented in the form of mean and variance of the structural response. The effects of material nonlinearity are included through the use of a rate-independent anisotropic plasticity formulation with the macroscopic point of view. Both ply-level and micromechanics-level random variables can be selected, the latter by means of the Aboudi micromechanics model. A number of sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. Experimental data is compared in many cases, and the Monte Carlo simulation method is used to check the probabilistic results. In general, the procedure is quite effective in modeling the mean and variance response of the linear and nonlinear behavior of laminated composite shells.

Engelstad, S. P.↗

NASA NTRS1986

High temperature stress-strain analysis

The objectives of the high-temperature structures program are threefold: to assist in the development of analytical tools needed to improve design analyses and procedures for the efficient and accurate prediction of the nonlinear structural response of hot-section components; to aid in the calibration, validation, and evaluation of the analytical tools by comparing predictions with experimental data; and to evaluate existing as well as advanced temperature and strain measurement instrumentation. As the analytical tools, test methods, tests, instrumentations, as well as data acquisition, management, and analysis methods are developed and evaluated, a proven, integrated analysis and experiment method will result in a more accurate prediction of the cyclic life of hot section components.

Thompson, Robert L.↗

NASA NTRS1983

Reduction methods for nonlinear steady-state thermal analysis

Hybrid analysis techniques and a problem adaptive computational algorithm are presented for predicting the nonlinear steady state temperature distribution in structures and solids. In the proposed techniques, the structure is discretized by using the finite element method. The vector of nodal temperatures is then expressed as a linear combination of a small number of global temperature modes (or basis vectors), and the Bubnov Galerkin technique is used to compute the amplitudes of the global modes. The global temperature modes (or basis vectors) are chosen to include the various order derivatives of the nodal temperature vector with respect to preselected path parameter(s). The potential of the proposed reduction methods for solution of large scale, nonlinear thermal problems is discussed and the effectiveness of the methods is demonstrated by means of numerical examples, including steady state conduction, convection, and radiation modes of heat transfer.

Noor, A. K.↗

NASA NTRS1985

Cyclic structural analyses of anisotropic turbine blades for reusable space propulsion systems

Turbine blades for reusable space propulsion systems are subject to severe thermomechanical loading cycles that result in large inelastic strains and very short lives. These components require the use of anisotropic high-temperature alloys to meet the safety and durability requirements of such systems. To assess the effects on blade life of material anisotropy, cyclic structural analyses are being performed for the first stage high-pressure fuel turbopump blade of the space shuttle main engine. The blade alloy is directionally solidified MAR-M 246 alloy. The analyses are based on a typical test stand engine cycle. Stress-strain histories at the airfoil critical location are computed using the MARC nonlinear finite-element computer code. The MARC solutions are compared to cyclic response predictions from a simplified structural analysis procedure developed at the NASA Lewis Research Center.

Manderscheid, J. M.↗

NASA NTRS1987

Thermo-elasto-viscoplastic analysis of problems in extension and shear

The problems of extension and shear behavior of structural elements made of carbon steel and subjected to large thermomechanical loads are investigated. The analysis is based on nonlinear geometric and constitutive relations, and is expressed in a rate form. The material constitutive equations are capable of reproducing all nonisothermal, elasto-viscoplastic characteristics. The results of the test problems show that: (1) the formulation can accommodate very large strains and rotations; (2) the model incorporates the simplification associated with rate-insensitive elastic response without losing the ability to model a rate-temperature dependent yield strength and plasticity; and (3) the formulation does not display oscillatory behavior in the stresses for the simple shear problem.

Riff, R.↗

NASA NTRS1988

Thermo-elasto-viscoplastic analysis of problems in extension and shear

Riff, R.↗

NASA NTRS1989

A numerical analysis of Stefan problems for generalized multi-dimensional phase-change structures using the enthalpy transforming model

An enthalpy transforming scheme is proposed to convert the energy equation into a nonlinear equation with the enthalpy, E, being the single dependent variable. The existing control-volume finite-difference approach is modified so it can be applied to the numerical performance of Stefan problems. The model is tested by applying it to a three-dimensional freezing problem. The numerical results are in agreement with those existing in the literature. The model and its algorithm are further applied to a three-dimensional moving heat source problem showing that the methodology is capable of handling complicated phase-change problems with fixed grids.

Cao, Yiding↗

NASA NTRS1990

On the instability of Goertler vortices to nonlinear travelling waves

Recent theoretical work by Hall and Seddougui (1989) has shown that strongly nonlinear, high wavenumber Goertler vortices developing within a boundary layer flow are susceptible to a secondary instability which takes the form of travelling waves confined to a thin region centered at the outer edge of the vortex. The case is considered in which the secondary mode could be satisfactorily described by a linear stability theory and herein the objective is to extend this investigation of Hall and Seddougui (1989) into the nonlinear regime. It was found that at this stage not only does the secondary mode become nonlinear but it also interacts with itself so as to modify the governing equations for the primary Goertler vortex. In this case then, the vortex and the travelling wave drive each other and, indeed, the whole flow structure is described by an infinite set of coupled, nonlinear differential equations. A Stuart-Watson type of weakly nonlinear analysis of these equations is undertaken and concluded, in particular, that on this basis there exist stable flow configurations in which the travelling mode is of finite amplitude. Implications of the findings for practical situations are discussed and it is shown that the theoretical conclusions drawn here are in good qualitative agreement with available experimental observations.

Seddougui, Sharon O.↗

NASA NTRS1993

Geometrically nonlinear design sensitivity analysis on parallel-vector high-performance computers

Parallel-vector solution strategies for generation and assembly of element matrices, solution of the resulted system of linear equations, calculations of the unbalanced loads, displacements, stresses, and design sensitivity analysis (DSA) are all incorporated into the Newton Raphson (NR) procedure for nonlinear finite element analysis and DSA. Numerical results are included to show the performance of the proposed method for structural analysis and DSA in a parallel-vector computer environment.

Baddourah, Majdi A.↗

NASA NTRS1993

Finite element analysis of structural engineering problems using a viscoplastic model incorporating two back stresses

The feasibility of a viscoplastic model incorporating two back stresses and a drag strength is investigated for performing nonlinear finite element analyses of structural engineering problems. To demonstrate suitability for nonlinear structural analyses, the model is implemented into a finite element program and analyses for several uniaxial and multiaxial problems are performed. Good agreement is shown between the results obtained using the finite element implementation and those obtained experimentally. The advantages of using advanced viscoplastic models for performing nonlinear finite element analyses of structural components are indicated.

Arya, Vinod K.↗

NASA NTRS1993

Turbine blade forced response prediction using FREPS

This paper describes a software system called FREPS (Forced REsponse Prediction System) that integrates structural dynamic, steady and unsteady aerodynamic analyses to efficiently predict the forced response dynamic stresses in axial flow turbomachinery blades due to aerodynamic and mechanical excitations. A flutter analysis capability is also incorporated into the system. The FREPS system performs aeroelastic analysis by modeling the motion of the blade in terms of its normal modes. The structural dynamic analysis is performed by a finite element code such as MSC/NASTRAN. The steady aerodynamic analysis is based on nonlinear potential theory and the unsteady aerodynamic analyses is based on the linearization of the non-uniform potential flow mean. The program description and presentation of the capabilities are reported herein. The effectiveness of the FREPS package is demonstrated on the High Pressure Oxygen Turbopump turbine of the Space Shuttle Main Engine. Both flutter and forced response analyses are performed and typical results are illustrated.

Murthy, Durbha, V.↗

NASA NTRS2000

Effect of Discontinuities and Uncertainties on the Response and Failure of Composite Structures

The overall goal of this research was to assess the effect of discontinuities and uncertainties on the nonlinear response and failure of composite structures subjected to combined mechanical and thermal loads. The four key elements of the study were: (1) development of simple and efficient procedures for the accurate determination of transverse shear and transverse normal stresses in structural sandwiches as well as in unstiffened and stiffened composite panels and shells; (2) study the effects of transverse stresses on the response, damage initiation and propagation in composite and sandwich structures; (3) use of hierarchical sensitivity coefficients to identify the major parameters that affect the response and damage in each of the different levels in the hierarchy (micro-mechanical, layer, panel, subcomponent and component levels); and (4) application of fuzzy set techniques to identify the range and variation of possible responses. The computational models developed were used in conjunction with experiments, to understand the physical phenomena associated with the nonlinear response and failure of composite and sandwich structures. A toolkit was developed for use in conjunction with deterministic analysis programs to help the designer in assessing the effect of uncertainties in the different computational model parameters on the variability of the response quantities.

Noor, Ahmed K.↗

NASA NTRS2015

Nonlinear Analysis and Preliminary Testing Results of a Hybrid Wing Body Center Section Test Article

A large test article was recently designed, analyzed, fabricated, and successfully tested up to the representative design ultimate loads to demonstrate that stiffened composite panels with through-the-thickness reinforcement are a viable option for the next generation large transport category aircraft, including non-conventional configurations such as the hybrid wing body. This paper focuses on finite element analysis and test data correlation of the hybrid wing body center section test article under mechanical, pressure and combined load conditions. Good agreement between predictive nonlinear finite element analysis and test data is found. Results indicate that a geometrically nonlinear analysis is needed to accurately capture the behavior of the non-circular pressurized and highly-stressed structure when the design approach permits local buckling.

Przekop, Adam↗

NASA NTRS2006

Estimation of Sonic Fatigue by Reduced-Order Finite Element Based Analyses

A computationally efficient, reduced-order method is presented for prediction of sonic fatigue of structures exhibiting geometrically nonlinear response. A procedure to determine the nonlinear modal stiffness using commercial finite element codes allows the coupled nonlinear equations of motion in physical degrees of freedom to be transformed to a smaller coupled system of equations in modal coordinates. The nonlinear modal system is first solved using a computationally light equivalent linearization solution to determine if the structure responds to the applied loading in a nonlinear fashion. If so, a higher fidelity numerical simulation in modal coordinates is undertaken to more accurately determine the nonlinear response. Comparisons of displacement and stress response obtained from the reduced-order analyses are made with results obtained from numerical simulation in physical degrees-of-freedom. Fatigue life predictions from nonlinear modal and physical simulations are made using the rainflow cycle counting method in a linear cumulative damage analysis. Results computed for a simple beam structure under a random acoustic loading demonstrate the effectiveness of the approach and compare favorably with results obtained from the solution in physical degrees-of-freedom.

Rizzi, Stephen A.↗

NASA NTRS1972

Dynamic response analysis of geometrically non-linear structures subjected to high impact.

Description of an efficient digital computer method for the determination of the propagation of elastic stresses and deformations in certain geometrically nonlinear structures subjected to high impact loading. The finite-element matrix displacement approach utilizing curved quadrilateral shell elements in conjunction with a nodewise predictor-corrector method employing Runge-Kutta extrapolation techniques has been adopted for the present solution. The related computer program written in FORTRAN V for the UNIVAC 1108 computer has proved to be effective for the solution of a range of practical problems including rectangular and cylindrical panels. Numerical results are presented for a relevant structure, the cell container, and the negative electrode of an impact-resistant battery subjected to high impact, simulating its free landing on a planetary surface.

Gupta, K. K.↗

NASA NTRS2003

Fully Nonlinear Modeling and Analysis of Precision Membranes

High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.

Pai, P. Frank↗

NASA NTRS1992

Buckling of imperfect, anisotropic, ring-stiffened cylinders under combined loads

The objectives of this study is to develop an analysis to predict loads of ring-stiffened anisotropic cylinders subject to axial compression, torsion and internal pressure. This structure is modeled as a branched shell. A nonlinear axisymmetric prebuckling equilibrium state is assumed which is amenable to exact solution within each branch. Axisymmetric geometric imperfections are included. Buckling displacements are represented by a Fourier series in the circumferential coordinate and the finite element method in the axial coordinate. Application of Trefftz criterion to the second variation of the total potential energy leads to a nonlinear eigenvalue problem for the buckling load and mode. Results are presented for both unstiffened and ring-stiffened cylinders in the form of buckling interaction diagrams. Imperfections can cause an unexpected buckling mode in the ring web which would not occur for the perfect structure, and pressurization diminishes the benefit of adding rings to the unstiffened shell to increase the buckling load. The implementation of the analysis methodology into a structural sizing algorithm is discussed.

Ley, Robert P.↗

NASA NTRS1989

Parallel linear equation solvers for finite element computations

The overall objective of this research is to develop efficient methods for the solution of linear and nonlinear systems of equations on parallel and supercomputers, and to apply these methods to the solution of problems in structural analysis. Attention has been given so far only to linear equations. The methods considered for the solution of the stiffness equation Kx=f have been Choleski factorization and the conjugate gradient iteration with SSOR and Incomplete Choleski preconditioning. More detail on these methods will be given on subsequent slides. These methods have been used to solve for the static displacements for the mast and panel focus problems in conjunction with the CSM testbed system based on NICE/SPAR.

Ortega, James M.↗