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NASA NTRS1991

Stacking-sequence optimization for buckling of laminated plates by integer programming

Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for a given total thickness and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily available software. This is in contrast to the continuous case, where the design variables are the thicknesses of layers with specified ply orientations, and the optimization problem is nonlinear. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-bound algorithm.

Haftka, Raphael T.↗

NASA NTRS1991

Hierarchic models for laminated plates

The research conducted in the formulation of hierarchic models for laminated plates is described. The work is an extension of the work done for laminated strips. The use of a single parameter, beta, is investigated that represents the degree to which the equilibrium equations of three dimensional elasticity are satisfied. The powers of beta identify members in the hierarchic sequence. Numerical examples that were analyzed with the proposed sequence of models are included. The results obtained for square plates with uniform loading and homogeneous boundary conditions are very encouraging. Several cross-ply and angle-ply laminates were evaluated and the results compared with those of the fully three dimensional model, computed using MSC/PROBE, and with previously reported work on laminated strips.

Szabo, Barna A.↗

NASA NTRS1990

Models of space averaged energetics of plates

The analysis of high frequency vibrations in plates is of particular interest in the study of structure borne noise in aircrafts. The current methods of analysis are either too expensive (finite element method) or may have a confidence band wider than desirable (Statistical Energy Analysis). An alternative technique to model the space and time averaged response of structural acoustics problems with enough detail to include all significant mechanisms of energy generation, transmission, and absorption is highly desirable. The focus of this paper is the development of a set of equations which govern the space and time averaged energy density in plates. To solve this equation, a new type of boundary value problem must be treated in terms of energy density variables using energy and intensity boundary conditions. A computer simulation verification study of the energy governing equation is performed. A finite element formulation of the new equations is also implemented and several test cases are analyzed and compared to analytical solutions.

Bouthier, O. M.↗

NASA NTRS1989

Response of laminated plates to non-stationary random excitation

The response of composite laminated plates subjected to nonstationary random excitation is determined. First-order shear deformation theory is used for the analysis of symmetric cross-ply and antisymmetric angle-ply plates. The time-dependent component of the forcing function is taken as a product of a well-defined, slowly varying envelope function, and a noise function, assumed to be white or narrow-band random excitation.

Cederbaum, Gabriel↗

NASA NTRS1990

Determination of refractive index of a simple negative, positive, or zero power lens using wedged plated interferometer

A nondestructive technique for measuring the refractive index of a negative lens using a wedged plate interferometer is described. The method can be also used for measuring the refractive index of convex or zero power lenses. Schematic diagrams are presented for the use of a wedged plate interferometer for measuring the refractive index of a concave lens and of a convex lens.

Shukla, R. P.↗

NASA NTRS1990

The relationship between plate velocity and trench viscosity in Newtonian and power-law subduction calculations

The relationship between oceanic trench viscosity and oceanic plate velocity is studied using a Newtonian rheology by varying the viscosity at the trench. The plate velocity is a function of the trench viscosity for fixed Rayleigh number and plate/slab viscosity. Slab velocities for non-Newtonian rheology calculations are significantly different from slab velocities from Newtonian rheology calculations at the same effective Rayleigh number. Both models give reasonable strain rates for the slab when compared with estimates of seismic strain rate. Non-Newtonian rheology eliminates the need for imposed weak zones and provides a self-consistent fluid dynamical mechanism for subduction in numerical convection models.

King, Scott D.↗

NASA NTRS1990

Thermal buckling and post-buckling of symmetric composite plates

The thermally induced buckling and postbuckling behavior of square and rectangular simply supported composite plates is examined using the Rayleigh-Ritz method in conjunction with the second variations of the total potential energy. Spatially uniform and nonuniform temperatures and laminates with material axes that are not aligned with the plate edges (skewed material axes) are considered. Results of the analysis are presented in graphic form.

Meyers, C. A.↗

NASA NTRS1991

Stacking-sequence optimization for buckling of laminated plates by integer programming

Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for given total thickness, and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily aviable software. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-bound algorithm.

Haftka, Raphael T.↗

NASA NTRS1991

A geometrically nonlinear analysis of interlaminar stresses in unsymmetrically laminated plates subjected to inplane mechanical loading

The present analysis of interlaminar stresses in unsymmetrically laminates plates gives attention to the linear elastic large-deflection response of square laminated composite plates subjected to either uniaxial tension or compression loading. The effects of Poisson-ratio and mutual-influence coefficient mismatching between adjacent layers is evaluated in both cross-ply and angle-ply, and symmetric and asymmetric laminates. A global/local analysis procedure is used to obtain improved free-edge depictions; the results obtained indicate that the out-of-plane deflections of the unsymmetric laminates reduce interlaminar shear stresses, while reducing interlaminar normal stresses in some laminates and increasing them in others.

Norwood, D. Scott↗

NASA NTRS1991

An improved error analysis of finite element solutions for postbuckled plates

The accurate calculation of stresses at boundaries and interfaces where FEM analysis may be unreliable is presently undertaken by an error analysis that derives a continuous approximation to discrete finite-element data, which can be differentiated to compute continuous stresses for component-failure predictions. An evaluation is conducted of this approximation in the context of the nonlinear PDEs. A novel interpolation formula which is a simple modification of the double Fourier sine series is used to reduce truncation errors near the rectangular plate boundary by means of an 'extended grid'. Results are presented from a FEM solution, a conventional double-Fourier series' continuous approximation, and a solution applying interpolation on the extended grid, which yields superior convergence properties near the plate boundaries.

Sistla, Rajaram↗

NASA NTRS1991

Finite element analysis of thermal post-buckling and vibrations of thermally buckled composite plates

A finite-element formulation is presented for the analysis of thermal postbuckling and free vibrations of thermally buckled, thin, rectangular, arbitrarily laminated, composite plates. The thermal load is considered to be a large steady-state temperature change over the plate. The equations of motion are derived from the principle of virtual work. The solution procedures are briefly discussed. Finite-element results are compared with existing isotropic and composite solutions. Examples studied include symmetric and antisymmetric angle-ply laminates and certain symmetric laminates.

Mei, Chuh↗

NASA NTRS1991

Variational finite element-tensor formulation for the large deflection random vibration of composite plates

A numerical integration routine is derived from a set of unified single step integration algorithms using a weighted satisfaction of the equilibrium equation governing the large deflection random response of laminated composite plates. The equilibrium equation is derived using a constant matrix large deflection finite-element formulation. In-plane inertia terms are considered in the formulation, however, rotary inertia terms are assumed negligible. Probability density, spectral density and autocorrelation functions of the maximum displacement and strain responses are presented for three acoustic excitation levels. Classical thin plate boundary conditions and pseudo white noise excitation are used in this investigation.

Robinson, Jay H.↗

NASA NTRS1989

Finite element large-amplitude free and forced vibrations of rectangular thin composite plates

A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite rectangular thin plates. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite rectangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, different boundary conditions, aspect ratios, lamination angles and number of plies are presented. The finite element results are compared with available approximate continuum solutions.

Chiang, C. K.↗

NASA NTRS1991

North American plate dynamics

Deformation within the North American plate in response to various tectonic processes is modeled using an elastic finite element analysis. The tectonic processes considered in the modeling include ridge forces associated with the normal thermal evolution of oceanic lithosphere, shear and normal stresses transmitted across transforms, normal stresses transmitted across convergent boundaries, stresses due to horizontal density contrasts within the continent, and shear tractions applied along the base of the plate. Model stresses are calculated with respect to a lithostatic reference stress state. Shear stresses transmitted across transform boundaries along the San Andreas and Caribbean are small, of the order of 5-10 MPa. Also, compressive stresses of the order of 5-10 MPa transmitted across the major transforms improve the fit to the data. Compressive stresses across convergent margins along the Aleutians and the Middle America trench are important.

Richardson, Randall M.↗

NASA NTRS1991

Tomography, the geoid and plate motions

The dynamics of the earth's mantle and its relationship to mantle structure as revealed by seismic tomography, the geoid, and plate motions are discussed in a critical review of U.S. research from the period 1987-1990. Sections are devoted to plates and mantle convection; seismic anomalies, flow, and the geoid; subducted slabs and the 670-km discontinuity; the physical properties of the mantle; plumes; and computational and experimental modeling efforts. Also included is a comprehensive bibliography for the period.

Gable, Carl W.↗

NASA NTRS1990

Experimental flaw detection by scattering of plate waves

The surface displacements of elastic waves scattered from a surface-breaking crack are measured with a capacitive transducer on a 2D plate, and comparisons with theoretical predictions are reported. The noncontacting detector has a wide and flat frequency response which measures the response of a glass plate to the propagation of Rayleigh-Lamb waves. A theoretical simulation of the surface displacements is generated by multiplying experimental traces with a cosine window, and Green's function is used to compute the source function. Power spectra are also recorded from the experiment to compare the results with a finite-element model of the crack, and good agreement is reported for results in both the time and frequency domains. The crack can be detected in the far field when the spacing of the receiver locations is small, and the transducer/probe appears to be a practical flaw-detection instrument.

Spetzler, Hartmut↗

NASA NTRS1992

Dual-Passband Microwave Dichroic Plates

Perforated metal plate with dielectric-filled holes acts as dual-passband dichroic microwave plate. Use of dielectric enables use of smaller, more-closely-spaced holes, reducing undesired diffraction-grating lobes. Arrangement and sizes of holes, distances between them, and material and dimensions of dielectric plugs chosen to satisfy design requirements.

Otoshi, Tom Y.↗

NASA NTRS1991

The first ANDES elements: 9-DOF plate bending triangles

New elements are derived to validate and assess the assumed natural deviatoric strain (ANDES) formulation. This is a brand new variant of the assumed natural strain (ANS) formulation of finite elements, which has recently attracted attention as an effective method for constructing high-performance elements for linear and nonlinear analysis. The ANDES formulation is based on an extended parametrized variational principle developed in recent publications. The key concept is that only the deviatoric part of the strains is assumed over the element whereas the mean strain part is discarded in favor of a constant stress assumption. Unlike conventional ANS elements, ANDES elements satisfy the individual element test (a stringent form of the patch test) a priori while retaining the favorable distortion-insensitivity properties of ANS elements. The first application of this formulation is the development of several Kirchhoff plate bending triangular elements with the standard nine degrees of freedom. Linear curvature variations are sampled along the three sides with the corners as gage reading points. These sample values are interpolated over the triangle using three schemes. Two schemes merge back to conventional ANS elements, one being identical to the Discrete Kirchhoff Triangle (DKT), whereas the third one produces two new ANDES elements. Numerical experiments indicate that one of the ANDES element is relatively insensitive to distortion compared to previously derived high-performance plate-bending elements, while retaining accuracy for nondistorted elements.

Militello, Carmelo↗