Engineering topics

Noor, Ahmed K.

Publications and source records attributed to Noor, Ahmed K..

At least 127 records · Page 7

NASA NTRS1989

Mixed finite element formulation for frictionless contact problems

Simple mixed finite element models and a computational procedure are presented for the solution of frictionless contact problems. The analytical formulation is based on a form of Reissner's large-rotation theory of the structure with the effect of transverse shear deformation included. The contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the internal forces (or stress resultants), the generalized displacements, and the Lagrange multipliers associated with the contact conditions. Numerical examples of axisymmetric deformations of a hemispherical shell and planar deformations of a circular ring are presented. Both structures are pressed against a rigid plate. Detailed information about the response of the structures is presented. The numerical studies demonstrate the high accuracy of the mixed models and the effectiveness of the computational procedure based on combining the geometrically nonlinear terms and the contact conditions in one iteration loop.

Noor, Ahmed K.↗

NASA NTRS1989

Partitioning strategy for efficient nonlinear finite element dynamic analysis on multiprocessor computers

A computational procedure is presented for the nonlinear dynamic analysis of unsymmetric structures on vector multiprocessor systems. The procedure is based on a novel hierarchical partitioning strategy in which the response of the unsymmetric and antisymmetric response vectors (modes), each obtained by using only a fraction of the degrees of freedom of the original finite element model. The three key elements of the procedure which result in high degree of concurrency throughout the solution process are: (1) mixed (or primitive variable) formulation with independent shape functions for the different fields; (2) operator splitting or restructuring of the discrete equations at each time step to delineate the symmetric and antisymmetric vectors constituting the response; and (3) two level iterative process for generating the response of the structure. An assessment is made of the effectiveness of the procedure on the CRAY X-MP/4 computers.

Noor, Ahmed K.↗

NASA NTRS1989

Mixed formulation for frictionless contact problems

Simple mixed finite element models and a computational precedure are presented for the solution of frictionless contact problems. The analytical formulation is based on a form of Reissner's large rotation theory of the structure with the effects of transverse shear deformation included. The contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the internal forces (stress resultants), the generalized displacements, and the Lagrange multipliers associated with the contact conditions. The element characteristic array are obtained by using a modified form of the two-field Hellinger-Reissner mixed variational principle. The internal forces and the Lagrange multipliers are allowed to be discontinuous at interelement boundaries. The Newton-Raphson iterative scheme is used for the solution of the nonlinear algebraic equations, and the determination of the contact area and the contact pressures.

Noor, Ahmed K.↗

NASA NTRS1989

Analysis of multilayered anisotropic plates - A new look at an old problem

The paper is concerned with the effects of variation in the lamination and geometric parameters of multilayered anisotropic plates on the accuracy of the static and vibrational responses predicted by six modeling approaches based on two-dimensional shear deformation theories. Extensive numerical results are presented for antisymmetrically laminated anisotropic rectangular plates. It is shown that, for most practical problems, the transverse shear deformation has a much more pronounced effect on the response of multilayered composite plates than that of transverse normal strain and stress. It is also shown that the accuracy of the predictions of the first-order deformation theory is strongly dependent on the values of the composite shear correction factors used.

Noor, Ahmed K.↗

NASA NTRS1989

Stress and free vibration analyses of multilayered composite plates

This paper presents a two-phase computational procedure for the accurate prediction of vibration frequencies, stresses, and deformations in simply supported bidirectional multilayered composite plates. The range of applicability of this procedure in terms of the plate's parameters is determined, and the potential of the proposed procedure for use in conjunction with large-scale finite element modeling of composite structures is discussed. It is shown that the use of the shear correction factors calculated by this procedure extends the range of the validity of the first-order shear deformation theory, used in the first phase of the procedure, to fairly thick multilayered plates with the h/L1 ratio of the order of 0.3.

Noor, Ahmed K.↗

NASA NTRS1989

A partitioning strategy for efficient nonlinear finite element dynamic analysis on multiprocessor computer

Noor, Ahmed K.↗

NASA NTRS1989

New computing systems and their impact on structural analysis and design

A review is given of the recent advances in computer technology that are likely to impact structural analysis and design. The computational needs for future structures technology are described. The characteristics of new and projected computing systems are summarized. Advances in programming environments, numerical algorithms, and computational strategies for new computing systems are reviewed, and a novel partitioning strategy is outlined for maximizing the degree of parallelism. The strategy is designed for computers with a shared memory and a small number of powerful processors (or a small number of clusters of medium-range processors). It is based on approximating the response of the structure by a combination of symmetric and antisymmetric response vectors, each obtained using a fraction of the degrees of freedom of the original finite element model. The strategy was implemented on the CRAY X-MP/4 and the Alliant FX/8 computers. For nonlinear dynamic problems on the CRAY X-MP with four CPUs, it resulted in an order of magnitude reduction in total analysis time, compared with the direct analysis on a single-CPU CRAY X-MP machine.

Noor, Ahmed K.↗

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 NTRS1989

State-of-the-art surveys on computational mechanics

Topics considered include advances in finite difference techniques for computational fluid dynamics, the spectral element methods for the incompressible Navier-Stokes equations, a review of recent developments in time integration, and advances and trends in element-by-element techniques. Also examined are the algebraic multigrid methods applied to problems in computational structural mechanics, grid generation for the solution of partial differential equations, advances in adaptive improvements, and new computing systems and their impact on computational mechanics.

Noor, Ahmed K.↗

NASA NTRS1989

New computing systems and their impact on computational mechanics

Recent advances in computer technology that are likely to impact computational mechanics are reviewed. The technical needs for computational mechanics technology are outlined. The major features of new and projected computing systems, including supersystems, parallel processing machines, special-purpose computing hardware, and small systems are described. Advances in programming environments, numerical algorithms, and computational strategies for new computing systems are reviewed, and a novel partitioning strategy is outlined for maximizing the degree of parallelism on multiprocessor computers with a shared memory.

Noor, Ahmed K.↗

NASA NTRS1989

Assessment of shear deformation theories for multilayered composite plates

A review is made of the different approaches used for modeling multilayered composite plates. Discussion focuses on different approaches for developing two-dimensional shear deformation theories; classification of two-dimensional theories based on introducing plausible displacement, strain and/or stress assumptions in the thickness direction; and first-order shear deformation theories based on linear displacement assumptions in the thickness coordinate. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of simply supported composite plates on the accuracy of the static and vibrational responses predicted by six different modeling approaches (based on two-dimensional shear deformation theories). The standard of comparison is taken to be the exact three-dimensional elasticity solutions. Some of the future directions for research on the modeling of multilayered composite plates are outlined.

Noor, Ahmed K.↗

NASA NTRS1989

Stress, vibration, and buckling of multilayered cylinders

An efficient computational method for lowering the cost of the free vibration, stress, and buckling analyses of multilayered composite cylinders is presented. The analytical methodology is based on the linear three-dimensional theory of elasticity where the cylinders are assumed to have simply supported curved edges, and the fibers of the different layers are either in the circumferential or in the longitudinal direction. The full equations of the finite element model are solved for a single pair of Fourier harmonics, and the response that corresponds to the other Fourier harmonics is generated utilizing a reduced system with considerably fewer degrees of freedom.

Noor, Ahmed K.↗

NASA NTRS1988

Reanalysis procedure for large structural systems

Global-basis-vector approximate reanalysis techniques for use in automated structural optimization schemes are developed and demonstrated. The vibrational response of a modified structure (MS) is estimated by lumping the design variables into a single tracing parameter, applying an operator splitting procedure to express the FEM equations of the MS in terms of the original-structure equations plus correction terms, and reducing the MS equations via a classical Bubnov-Galerkin scheme. The sensitivity of the vibrational response to structural modifications is evaluated, and the relationship between this method and the preconditioned conjugate-gradient method (Noor and Peters, 1988) is explored. Numerical results for linear static and free vibration problems involving beamlike lattices, double-layered hexahedral grids, and structural gridworks are presented in tables and graphs and briefly characterized.

Noor, Ahmed K.↗

NASA NTRS1988

Stress and vibraton analyses of anisotropic shells of revolution

An efficient computational strategy is presented for reducing the cost of the stress and free vibration analyses of laminated anisotropic shells of revolution. The analytical formulation is based on a form of the Sanders-Budiansky shell theory including the effects of both the transverse shear deformation and the laminated anisotropic material response. The fundamental unknowns consist of the eight strain components, the eight stress resultants and the five generalized displacements of the shell. Each of the shell variables is expressed in terms of trigonometric functions (Fourier series) in the circumferential co-ordinate, and a three-field mixed finite element model is used for the discretization in the meridional direction. The shell response associated with a range of Fourier harmonics is approximated by a linear combination of a few global approximation vectors, which are generated at a particular value of the Fourier harmonic, within that range. The full equations of the finite element model are solved for only a single Fourier harmonic, and the response corresponding to the other Fourier harmonics is generated using a reduced system of equations with considerably fewer degrees of freedom.

Noor, Ahmed K.↗

NASA NTRS1988

Advances in contact algorithms and their application to tires

Currently used techniques for tire contact analysis are reviewed. Discussion focuses on the different techniques used in modeling frictional forces and the treatment of contact conditions. A status report is presented on a new computational strategy for the modeling and analysis of tires, including the solution of the contact problem. The key elements of the proposed strategy are: (1) use of semianalytic mixed finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynomials in the meridional direction; (2) use of perturbed Lagrangian formulation for the determination of the contact area and pressure; and (3) application of multilevel iterative procedures and reduction techniques to generate the response of the tire. Numerical results are presented to demonstrate the effectiveness of a proposed procedure for generating the tire response associated with different Fourier harmonics.

Noor, Ahmed K.↗

NASA NTRS1988

Error indicators and accuracy improvements of finite element solutions

Practical and reliable estimators of the discretization errors in engineering problems are developed. Error indicators for identifying the regions or elements of the solution domain which are likely to have the largest discretization errors are presented, and a simple computational procedure for improving the accuracy of the finite element solutions for shell problems is given. The similarities between the proposed procedure and a preconditioned conjugate gradient (PCG) technique are identified and exploited to generate pointwise error indicators from the PCG technique. Numerical examples in the linear static analysis of shells are presented.

Noor, Ahmed K.↗

NASA NTRS1988

Continuum modeling of large lattice structures: Status and projections

The status and some recent developments of continuum modeling for large repetitive lattice structures are summarized. Discussion focuses on a number of aspects including definition of an effective substitute continuum; characterization of the continuum model; and the different approaches for generating the properties of the continuum, namely, the constitutive matrix, the matrix of mass densities, and the matrix of thermal coefficients. Also, a simple approach is presented for generating the continuum properties. The approach can be used to generate analytic and/or numerical values of the continuum properties.

Noor, Ahmed K.↗

NASA NTRS1988

A computational strategy for making complicated structural problems simple

An effective computational strategy is presented for the analysis of large and complex structures. The strategy is based on generating the response of the complex structure using large perturbations from that of a lower-order (simpler) model associated with a simpler structure (or a simpler mathematical/discrete model of the original structure). The three key elements of the strategy are: (a) mixed (or primitive variable) formulation with the fundamental unknowns consisting of generalized displacements and stress parameters; (2) operator splitting, or a reduction method to relate the arrays and degrees of freedom of the original complex structure ot those of the simpler system; and (3) efficient iterative process for the generation of the response of the complex structure starting from that of the simpler system. The effectiveness of the proposed strategy is demonstrated by means of two numerical examples.

Noor, Ahmed K.↗