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At least 235 records · Page 13

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NASA NTRS1978

Programs for analysis and resizing of complex structures

The paper describes the PARS (Programs for Analysis and Resizing of Structures) system. PARS is a user oriented system of programs for the minimum weight design of structures modeled by finite elements and subject to stress, displacement, flutter and thermal constraints. The system is built around SPAR - an efficient and modular general purpose finite element program, and consists of a series of processors that communicate through the use of a data base. An efficient optimizer based on the Sequence of Unconstrained Minimization Technique (SUMT) with an extended interior penalty function and Newton's method is used. Several problems are presented for demonstration of the system capabilities.

Haftka, R. T.↗

NASA NTRS1979

A cubic extended interior penalty function for structural optimization

This paper describes an optimization procedure for the minimum weight design of complex structures. The procedure is based on a new cubic extended interior penalty function (CEIPF) used with the sequence of unconstrained minimization technique (SUMT) and Newton's method. The Hessian matrix of the penalty function is approximated using only constraints and their derivatives. The CEIPF is designed to minimize the error in the approximation of the Hessian matrix, and as a result the number of structural analyses required is small and independent of the number of design variables. Three example problems are reported. The number of structural analyses is reduced by as much as 50 per cent below previously reported results.

Prasad, B.↗

NASA NTRS1980

Research in nonlinear structural and solid mechanics

Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.

Mccomb, H. G., Jr.↗

NASA NTRS1979

A general algorithm for the solution of Kepler's equation for elliptic orbits

An efficient algorithm is presented for the solution of Kepler's equation f(E)=E-M-e sin E=0, where e is the eccentricity, M the mean anomaly and E the eccentric anomaly. This algorithm is based on simple initial approximations that are cubics in M, and an iterative scheme that is a slight generalization of the Newton-Raphson method. Extensive testing of this algorithm has been performed on the UNIVAC 1108 computer. Solutions for 20,000 pairs of values of e and M show that for single precision, 42.0% of the cases require one iteration, 57.8% two and 0.2% three. For double precision one additional iteration is required.

Ng, E. W.↗

NASA NTRS1980

Preliminary design of composite wing-box structures for global damage tolerance

A procedure is presented that incorporates the influence of potential global damage conditions into the design process for minimum-mass wing-box structures. The procedure is based on mathematical-programming optimization techniques. Material-strength, minimum-gage, and panel-buckling constraints are introduced by penalty functions, and Newton's method with approximate second derivatives of the penalty terms is used as the search algorithm to obtain minimum-mass designs. A potential global damage condition is represented by a structural model with the damaged components removed. Example minimum-mass designs are obtained that simultaneously satisfy the constraints of the damaged and undamaged configurations of both graphite-epoxy and aluminum wing-box structural models. These examples are designed with and without the influence of potential damage conditions, and results indicate that for equal mass cases the residual strength of a damaged structure is higher when the influence of potential damage is properly included in the design from the outset. Results of these examples also identify the minimum structural mass increase required to increase residual strength levels.

Starnes, J. H., Jr.↗

NASA NTRS1982

Postbuckling of orthotropic composite plates loaded in compression

The nonlinear large deflection equations of von Karman are written for 'specially' orthotropic plates. The equations are then manipulated to determine the parameters required to establish postbuckling behavior. It is found that only two new parameters are needed beyond those required for buckling. By assuming trigonometric functions in one direction, the plate equations are converted into ordinary nonlinear differential equations which are solved numerically using a two point boundary problem solver that makes use of Newton's method. The postbuckling behavior is obtained for simply supported and clamped, long, rectangular, orthotropic plates covering the complete range of dimensions and material properties.

Stein, M.↗

NASA NTRS1981

A family of solution algorithms for nonlinear structural analysis based on relaxation equations

A family of hierarchical algorithms for nonlinear structural equations are presented. The algorithms are based on the Davidenko-Branin type homotopy and shown to yield consistent hierarchical perturbation equations. The algorithms appear to be particularly suitable to problems involving bifurcation and limit point calculations. An important by-product of the algorithms is that it provides a systematic and economical means for computing the stepsize at each iteration stage when a Newton-like method is employed to solve the systems of equations. Some sample problems are provided to illustrate the characteristics of the algorithms.

Park, K. C.↗

NASA NTRS1983

Postbuckling of long orthotropic plates in combined shear and compression

The nonlinear large-deflection partial differential equations of von karman for orthotropic plates loaded in combined shear and compression are converted into a set of first-order nonlinear ordinary differential equations by assuming trigonometric functions in one direction. These equations are solved numerically using a two point boundary problem solver which makes use of Newton's method. Results are obtained which determine the postbuckling behavior of rectangular plates with loading up to about three times the buckling load. Both isotropic and orthotropic composite plates are considered. Results show that orthotropic plates may behave quite differently than isotropic plates and that in-plane boundary conditions are important for plates loaded in shear.

Stein, M.↗

NASA NTRS1984

Steady viscous flow past a circular cylinder

Viscous flow past a circular cylinder becomes unstable around Reynolds number Re = 40. With a numerical technique based on Newton's method and made possible by the use of a supercomputer, steady (but unstable) solutions have been calculated up to Re = 400. It is found that the wake continues to grow in length approximately linearly with Re. However, in conflict with available asymptotic predictions, the width starts to increase very rapidly around Re = 300. All numerical calculations have been performed on the CDC CYBER 205 at the CDC Service Center in Arden Hills, Minnesota.

Fornberg, B.↗

NASA NTRS1984

Forced stationary solutions in a barotropic channel: Multiple equilibria and theory of nonlinear resonance

A barotropic flow over sinusoidal topography in a beta channel in the presence of forcing and dissipation was studied. The work is divided into two parts: (1) computation of the stationary solutions of the model, by Newton's method together with a finite difference approximation, and comparison of solutions with the solutions of the linear theory; (2) development of a nonlinear theory that reproduce the numerical solutions.

Rambaldi, S.↗

NASA NTRS1984

Analytical results for postbuckling behavior of plates in compression and shear

The postbuckling behavior of long rectangular isotropic and orthotropic plates is determined. By assuming trigonometric functions in one direction, the nonlinear partial differential equations of von Karman large deflection plate theory are converted into nonlinear ordinary differential equations. The ordinary differential equations are solved numerically using an available boundary value problem solver which makes use of Newton's method. Results for longitudinal compression show different postbuckling behavior between isotropic and orthotropic plates. Results for shear show that change in inplane edge constraints can cause large change in postbuckling stiffness.

Stein, M.↗

NASA NTRS1983

Finite element calculation of buoyancy-driven convection near a melt/solid phase boundary

Two iterative schemes based on the mixed finite element method are developed for analyzing steady natural convection in a melt adjacent to its solid phase. The simplest method decouples the calculation of the field variables and the shape of the melt/solid interface into two interlocked iterations that are performed successively. The second method uses Newton's iteration to solve simultaneously for both types of unknowns and has a quadratic convergence rate. Results for a model problem of melt and solid in a cylindrical ampoule show the Newton algorithm to be a factor of three more efficient.

Chang, C. J.↗

NASA NTRS1984

An improved computational approach for multilevel optimum design

A penalty-function algorithm employing Newton's method with approximate second derivatives (Haftka and Starnes, 1980) is developed for two-level hierarchical design optimization problems. The difficulties posed by discontinuous behavior in typical multilevel problems are explained and illustrated for the case of a three-bar truss; the algorithm is formulated; and its advantages are demonstrated in the problem of a portal framework having three beams (described by six cross-section parameters), subjected to two loading conditions, and to be constructed in six different materials for comparison. The final design parameters are listed in a table.

Haftka, R. T.↗

NASA NTRS1985

Structural parameter identification of distributed systems using finite element approximation

A system identification technique is developed for classes of distributed systems using finite element approximations. Vibrating systems represented by partial differential equations have physical parameters associated with mass, stiffness, and damping distributions which need to be known in order to properly control and design mathematical models of the system. In order to identify these parameters a weighted least-squares algorithm and modified Newton-Raphson method is used for the identification process. The theory and technique is demonstrated by estimating the system parameters of a vibrating cantilever beam made up of several different structural properties.

Lee, K. Y.↗

NASA NTRS1986

Rapid computation of chemical equilibrium composition - An application to hydrocarbon combustion

A scheme for rapidly computing the chemical equilibrium composition of hydrocarbon combustion products is derived. A set of ten governing equations is reduced to a single equation that is solved by the Newton iteration method. Computation speeds are approximately 80 times faster than the often used free-energy minimization method. The general approach also has application to many other chemical systems.

Erickson, W. D.↗

NASA NTRS1985

Analytical results for post-buckling behaviour of plates in compression and in shear

Stein, M.↗

NASA NTRS1987

Numerical simulations of trailing vortex bursting

Solutions of the steady-state Navier-Stokes equations for the axisymmetric bursting of a laminar trailing vortex are computed with Newton's method and the pseudo-arc length continuation method for wide ranges of vortex strength and Reynolds number. The results indicate that a trailing vortex can undergo a transition from a state in which the core slowly diffuses to a state marked by large amplitude, spatial oscillations of core radius and core axial velocity. At the transition point the core grows rapidly in size. This event is interpreted as vortex bursting. The results also suggest that when the maximum core swirl velocity is sufficiently large the centerline axial flow downstream of transition will be reversed.

Beran, Philip S.↗

NASA NTRS1988

Calculation of symmetric and asymmetric vortex seperation on cones and tangent ogives based on discrete vortex models

An inviscid discrete vortex model, with newly derived expressions for the tangential velocity imposed at the separation points, is used to investigate the symmetric and asymmetric vortex separation on cones and tangent ogives. The circumferential locations of separation are taken from experimental data. Based on a slender body theory, the resulting simultaneous nonlinear algebraic equations in a cross-flow plane are solved with Broyden's modified Newton-Raphson method. Total force coefficients are obtained through momentum principle with new expressions for nonconical flow. It is shown through the method of function deflation that multiple solutions exist at large enough angles of attack, even with symmetric separation points. These additional solutions are asymmetric in vortex separation and produce side force coefficients which agree well with data for cones and tangent ogives.

Chin, S.↗