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NASA NTRS1972

Study of effects of design details on structural response to acoustic excitation

The normal mode vibration characteristics of one-dimensional and two-dimensional panel arrays were investigated analytically and experimentally. The finite element displacement method was used to formulate the structural models. The structural models include a stiffness and consistent mass matrix for thin-walled open-section beams not previously reported, and a modification of a rectangular plate bending element to include a fundamental interior mode for the element as a generalized coordinate. Provision for adding lumped masses to represent accelerometers is also included. For the one-dimensional panel, the normal mode stress resultants are obtained by integrating the equilibrium equations directly. For the two-dimensional panel arrays, the solution for the stress resultants in the cover sheet was attempted by introducing stress functions dependent upon the displacement field of the plate element. This approach, although incomplete, is a natural extension of the one-dimensional analysis for plate elements. The exerimental program which was used to verify the analysis is described and experimental results are compared with the analysis.

Rudder, F. F., Jr.↗

NASA NTRS1973

Assuring reliability program effectiveness.

An attempt is made to provide simple identification and description of techniques that have proved to be most useful either in developing a new product or in improving reliability of an established product. The first reliability task is obtaining and organizing parts failure rate data. Other tasks are parts screening, tabulation of general failure rates, preventive maintenance, prediction of new product reliability, and statistical demonstration of achieved reliability. Five principal tasks for improving reliability involve the physics of failure research, derating of internal stresses, control of external stresses, functional redundancy, and failure effects control. A final task is the training and motivation of reliability specialist engineers.

Ball, L. W.↗

NASA NTRS1972

Large amplitude flexural vibration of thin elastic flat plates and shells

The general equations governing the large amplitude flexural vibration of any thin elastic shell using curvilinear orthogonal coordinates are derived and consist of two coupled, nonlinear, partial differential equations in the normal displacement w and the stress function F. From these equations, the governing equations for the case of shells of revolution or flat plates can be readily obtained as special cases. The material of the shell or plate is isotropic and homogeneous and Hooke's law for the two-dimensional case is valid. It is suggested that the difference between the hardening type of nonlinearity in the case of flat plates and straight beams and the softening type of nonlinearity in the case of shells and rings can, in general, be traced to the amount of curvature present in the underformed median surface of the structure concerned.

Pandalia, K. A. V.↗

NASA NTRS1978

Application of the method of integral relations to boundary layer flows over blunt bodies

Calculations of boundary layer flows past blunt bodies at angles of incidence are presented. Using the method of integral relations together with the method of lines, the full three-dimensional boundary layer equations are reduced to a system of first-order ordinary differential equations. The streamwise shear stress function and the cross-flow velocity component are represented as suitable functions of the streamwise velocity component. The role of the zone of dependence is automatically satisfied by the choice of differencing in the method of lines. Solutions correct to the second order are obtained in the positive shear region for flow over an ellipsoid at 30-deg incidence. The results are compared with corresponding finite difference solutions.

Modarress, D.↗

NASA NTRS1979

Influence of phase cancellation and pulse shape artifacts on ultrasonic spectrum analysis

Both continuous wave and Fourier transformed pulse ultrasonic spectroscopy are being applied to material and flow characterization. Ideal samples and flaws (flat, parallel, and homogeneous) and ideal ultrasonic apparatus (producing delta function stress waves) provide acoustic spectra which can be partially inverted. However, in the presence of material inhomogeneity, lack of sample flatness or parallelism, or finite risetime pulses, the spectra become quite complex and produce phase cancellations at the transducer as well as pulse shape spectral artifacts. In this paper, we examine the nature of these artifacts for both simple and practical samples. Sample spectra are contrasted for several different transducer/electronic systems. Spectra obtained with a phase insensitive acousto-electric transducer (AET) combined with a frequency tracked tone-burst spectroscopy (TBS) method are presented. Analysis of the test configuration is shown to produce spectra consistent with that obtained with the AET-TBS combination.

Heyman, J. S.↗

NASA NTRS1979

Boundary layer thermal stresses in angle-ply composite laminates

Boundary-layer thermal stress singularities and distributions of angle-ply composite laminates under uniform thermal loading are investigated through a system of sixth-order governing partial differential equations developed with the aid of the anisotropic elasticity field equations and Lekhnitskii's complex stress functions. Results are presented for cases of various angle-ply graphite/epoxy laminates, and it is shown that the boundary-layer thickness depends on the degree of anisotropy of each individual lamina, thermomechanical properties of each ply, and the relative thickness of adjacent layers.

Wang, S. S.↗

NASA NTRS1982

Effects of unsteady free-stream velocity and free-stream turbulence at a stagnation point

The combined effects of transient free stream velocity and turbulence at a stagnation point on a cylinder situated in a crossflow is investigated analytically, and a model is formulated for the eddy diffusivity induced by free-stream turbulence. The steepest descent method is used to integrate the governing momentum expression, and numerical solutions are given for the unsteady wall shear stress function for specific free-stream transients. It is found after correlation of the results by means of a new turbulence parameter that wall friction increases with increasing free-stream turbulence intensity, and that the friction factor increases with increasing reduced frequency of oscillation values.

Gorla, R. S. R.↗

NASA NTRS1982

Wide range weight functions for the strip with a single edge crack

A closed form expression for the weight function for a strip with a single edge crack is presented. The expression is valid for relative crack lengths from zero to unity. It is based on the assumption that the shape of an opened edge crack can be approximated by a conic section. The results agree well with published values for weight functions, stress intensity factors, and crack mouth opening displacements.

Orange, T. W.↗

NASA NTRS1984

An Improved Analysis of the Thermal Buckling of Silicon Sheet

Buckling problems on the production of wide and thin silicon sheet are discussed. Buckling occurs in all of the processes which are investigated for their potential in mass producing wide silicon sheet for use in making solar cells. It is a fact that the processes which produce good ribbon 2 cm in width do not yield the same quality product at 10 cm in width. Buckling develops precisely because the sheets are wide and very very thin. The buckling of very thin cantilever plates due to temperature variations in the axial direction is considered. The temperature variation in the width direction was determined. Axial temperature variations which cause very thin plates to buckle in a torsional mode are demonstrated. It is assumed that the particular variation of the stress function in the width direction and thereafter the analysis is exact.

Dillon, O. W., Jr.↗

NASA NTRS1985

Calculation of flow about posts and powerhead model

A three dimensional analysis of the non-uniform flow around the liquid oxygen (LOX) posts in the Space Shuttle Main Engine (SSME) powerhead was performed to determine possible factors contributing to the failure of the posts. Also performed was three dimensional numerical fluid flow analysis of the high pressure fuel turbopump (HPFTP) exhaust system, consisting of the turnaround duct (TAD), two-duct hot gas manifold (HGM), and the Version B transfer ducts. The analysis was conducted in the following manner: (1) modeling the flow around a single and small clusters (2 to 10) of posts; (2) modeling the velocity field in the cross plane; and (3) modeling the entire flow region with a three dimensional network type model. Shear stress functions which will permit viscous analysis without requiring excessive numbers of computational grid points were developed. These wall functions, laminar and turbulent, have been compared to standard Blasius solutions and are directly applicable to the cylinder in cross flow class of problems to which the LOX post problem belongs.

Anderson, P. G.↗

NASA NTRS1985

Wide-range weight functions for the strip with a single edge crack

Orange, T. W.↗

NASA NTRS1985

Three-dimensional hybrid-stress finite element analysis of composite laminates with cracks and cutouts

A three-dimensional hybrid-stress finite element analysis of composite laminates containing cutouts and cracks is presented. Fully three-dimensional, hexahedral isoparametric elements of the hybrid-stress model are formulated on the basis of the Hellinger-Reissner variational principle. Traction-free edges, cutouts, and crack surfaces are modeled by imposition of exact traction boundary conditions along element surfaces. Special boundary and surface elements are constructed by introducing proper constraints on assumed stress functions. The Lagrangian multiplier technique is used to enforce ply-interface continuity conditions in hybrid bimaterial composite elements for modeling the interface region in a composite laminate. Two examples are given to illustrate the capability of the present method of approach: (1) the well-known delamination problem in an angle-ply laminate, and (2) the important problem of a composite laminate containing a circular hole. Results are presented in detail for each case. Implications of interlaminar and intralaminar crack initiation, growth and fracture in composites containing cracks and cutouts are discussed.

Wang, S. S.↗

NASA NTRS1986

Design sensitivity analysis using EAL. Part 1: Conventional design parameters

A numerical implementation of design sensitivity analysis of builtup structures is presented, using the versatility and convenience of an existing finite element structural analysis code and its database management system. The finite element code used in the implemenatation presented is the Engineering Analysis Language (EAL), which is based on a hybrid method of analysis. It was shown that design sensitivity computations can be carried out using the database management system of EAL, without writing a separate program and a separate database. Conventional (sizing) design parameters such as cross-sectional area of beams or thickness of plates and plane elastic solid components are considered. Compliance, displacement, and stress functionals are considered as performance criteria. The method presented is being extended to implement shape design sensitivity analysis using a domain method and a design component method.

Dopker, B.↗

NASA NTRS1986

Design sensitivity analysis using EAL. Part 2: Shape design parameters

A numerical implementation of shape design sensitivity analysis of built-up structures is presented, using the versatility and convenience of an existing finite element structural analysis code and its data base management system. This report is a continuation of a previous report on conventional design parameters. The finite element code used in the implementation presented is the Engineering Analysis Language (EAL), which is based on a hybrid analysis method. It has been shown that shape design sensitivity computations can be carried out using the database management system of EAL, without writing a separate program and a separate data base. The material derivative concept of continuum mechanics and an adjoint variable method of design sensitivity analysis are used to derive shape design sensitivity information of structural performances. A domain method of shape design sensitivity analysis and a design component method are used. Displacement and stress functionals are considered as performance criteria.

Dopker, B.↗

NASA NTRS1987

Calculation of stresses and forces between the skin and stiffener in composite panels

A methodology for computing the stresses at the interface between the skin and stiffener in stiffened composite panels is described. The methodology is based on finite-element analyses and on elasticity solution. The finite-element analyses are standard, while the elasticity solution is based on eigenvalue expansions of the stress function. The eigenvalue expansions are assumed to be valid in the local region where the stiffener flange terminates. The local elasticity solution is coupled to the global finite-element analysis using collocation on the boundary of the local region. Accuracy and convergence of the method are discussed and several examples of its utility are presented.

Hyer, M. W.↗

NASA NTRS1987

Determination of calibration constants for the hole-drilling residual stress measurement technique applied to orthotropic composites. I - Theoretical considerations

The hole-drilling technique for the measurement of residual stresses using electrical resistance strain gages has been widely used for isotropic materials and has been adopted by the ASTM as a standard method. For thin isotropic plates, with a hole drilled through the thickness, the idealized hole-drilling calibration constants are obtained by making use of the well-known Kirsch's solution. In this paper, an analogous attempt is made to theoretically determine the three idealized hole-drilling calibration constants for thin orthotropic materials by employing Savin's (1961) complex stress function approach.

Prasad, C. B.↗

NASA NTRS1988

An improved boundary force method for analyzing cracked anisotropic materials

The Boundary Force Method (BFM), a form of indirect boundary element method, is used to analyze composite laminates with cracks. The BFM uses the orthotropic elasticity solution for a concentrated horizontal and vertical force and a moment applied at a point in a cracked, infinite sheet as the fundamental solution. The necessary stress functions for this fundamental solution were formulated using the complex variable theory of orthotropic elasticity. The current method is an improvement over a previous method using only forces and no moment. The improved method was verified by comparing it to accepted solutions for a finite-width, center-crack specimen subjected to uniaxial tension. Four graphite/epoxy laminates were used: (0 + or - 45/90)sub s, (0), (+ or - 45)sub s, and (+ or - 30)sub s. The BFM results agreed well with accepted solutions. Convergence studies showed that with the addition of the moment in the fundamental solution, the number of boundary elements required for a converged solution was significantly reduced. Parametric studies were done for two configurations for which no orthotropic solutions are currently available; a single edge crack and an inclined single edge crack.

Tan, Paul W.↗

NASA NTRS1989

An improved boundary force method for analysing cracked anisotropic materials

The Boundary Force Method (BFM), a form of indirect boundary element method, is used to analyze composite laminates with cracks. The BFM uses the orthotropic elasticity solution for a concentrated horizontal and vertical force and a moment applied at a point in a cracked, infinite sheet as the fundamental solution. The necessary stress functions for this fundamental solution were formulated using the complex variables theory of orthotropic elasticity. The current method is an improvement over a previous method using only forces and no moment. The improved method was verified by comparing it to accepted solutions for a finite-width, center-crack specimen subjected to uniaxial tension. Four graphite/epoxy laminates were used: (0 + or - 45/90)sub s, (0), (+ or - 45)sub s, and (+ or - 30)sub s. The BFM results agreed well with accepted solutions. Convergence studies showed that with the addition of the moment in the fundamental solution, the number of boundary elements required for a converged solution was significantly reduced. Parametric studies were done for two configurations for which no orthotropic solutions are currently available; a single edge crack and an inclined single edge crack.

Tan, P. W.↗