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NASA NTRS2011

Effect of Boundary Conditions on the Axial Compression Buckling of Homogeneous Orthotropic Composite Cylinders in the Long Column Range

Buckling loads for long isotropic and laminated cylinders are calculated based on Euler, Fluegge and Donnell's equations. Results from these methods are presented using simple parameters useful for fundamental design work. Buckling loads for two types of simply supported boundary conditions are calculated using finite element methods for comparison to select cases of the closed form solution. Results indicate that relying on Donnell theory can result in an over-prediction of buckling loads by as much as 40% in isotropic materials.

Mikulas, Martin M., Jr.↗

NASA NTRS1986

Preconditioned conjugate residual methods for the solution of spectral equations

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

Wong, Y. S.↗

NASA NTRS1987

An approximate semi-analytical method for prediction of interlaminar shear stresses in an arbitrarily laminated thick plate

An approximate semianalytical method for determination of interlaminar shear stress distribution through the thickness of an arbitrarily laminated thick plate has been presented. The method is based on the assumptions of transverse inextensibility and layerwise constant shear angle theory (LCST) and utilizes an assumed quadratic displacement potential energy based finite element method (FEM). Centroid of the triangular surface has been proved from a rigorous mathematical point of view (Aubin-Nitsche theory), to be the point of exceptional accuracy for the interlaminar shear stresses. Numerical results indicate close agreement with the available three-dimensional elasticity theory solutions. A comparison between the present theory and that due to an assumed stress hybrid FEM suggest that the (normal) traction-free-edge condition is not satisfied in the latter approach. Furthermore, the present paper is the first to present the results for interlaminar shear stresses in a two-layer thick square plate of balanced unsymmetric angle-ply construction. A comparison with the recently proposed Equilibrium Method (EM) indicates the superiority of the present method, because the latter assures faster convergence as well as simultaneous vanishing of the transverse shear stresses on both of the exposed surfaces of the laminate. Superiority of the present method over the EM, in the case of a symmetric laminate, is limited to faster convergence alone. It has also been demonstrated that the combination of the present method and the reduced (quadratic order) numerical integration scheme yields convergence of the interlaminar shear stresses almost as rapidly as that of the nodal displacements, in the case of a thin plate.

Chaudhuri, Reaz A.↗

NASA NTRS1999

Experimentally Determined Crack Location and Mixed Mode Stress Intensity Factors

This presentation first examines five strain field equations: the two modes of the Westergaard equations, and a mixed mode; the generalized coordinate system, and the significance testing of coefficients. It also discusses the weighted multiple linear least squares method, which shows why it is difficult to find the crack tip. The presentation then discusses the experiments to examine stress intensity. Lastly, comparison of finite element method results and experimental results is reviewed.

Zachary, Loren W.↗

NASA NTRS1989

Global functions in global-local finite-element analysis of localized stresses in prismatic structures

An important consideration in the global local finite-element method (GLFEM) is the availability of global functions for the given problem. The role and mathematical requirements of these global functions in a GLFEM analysis of localized stress states in prismatic structures are discussed. A method is described for determining these global functions. Underlying this method are theorems due to Toupin and Knowles on strain energy decay rates, which are related to a quantitative expression of Saint-Venant's principle. It is mentioned that a mathematically complete set of global functions can be generated, so that any arbitrary interface condition between the finite element and global subregions can be represented. Convergence to the true behavior can be achieved with increasing global functions and finite-element degrees of freedom. Specific attention is devoted to mathematically two-dimensional and three-dimensional prismatic structures. Comments are offered on the GLFEM analysis of NASA flat panel with a discontinuous stiffener. Methods for determining global functions for other effects are also indicated, such as steady-state dynamics and bodies under initial stress.

Dong, Stanley B.↗

NASA NTRS1985

Shape design sensitivity analysis using domain information

A numerical method for obtaining accurate shape design sensitivity information for built-up structures is developed and demonstrated through analysis of examples. The basic character of the finite element method, which gives more accurate domain information than boundary information, is utilized for shape design sensitivity improvement. A domain approach for shape design sensitivity analysis of built-up structures is derived using the material derivative idea of structural mechanics and the adjoint variable method of design sensitivity analysis. Velocity elements and B-spline curves are introduced to alleviate difficulties in generating domain velocity fields. The regularity requirements of the design velocity field are studied.

Seong, Hwal-Gyeong↗

NASA NTRS1996

Radiation Characteristics of Cavity Backed Aperture Antennas in Finite Ground Plane Using the Hybrid FEM/MoM Technique and Geometrical Theory of Diffraction

A technique using hybrid Finite Element Method (FEM)/Method of Moments (MoM), and Geometrical Theory of Diffraction (GTD) is presented to analyze the radiation characteristics of cavity fed aperture antennas in a finite ground plane. The cavity which excites the aperture is assumed to be fed by a cylindrical transmission line. The electromagnetic (EM) fields inside the cavity are obtained using FEM. The EM fields and their normal derivatives required for FEM solution are obtained using (1) the modal expansion in the feed region and (2) the MoM for the radiating aperture region(assuming an infinite ground plane). The finiteness of the ground plane is taken into account using GTD. The input admittance of open ended circular, rectangular, and coaxial line radiating into free space through an infinite ground plane are computed and compared with earlier published results. Radiation characteristics of a coaxial cavity fed circular aperture in a finite rectangular ground plane are verified with experimental results.

Reddy, C. J.↗

NASA NTRS1994

A case study of analysis methods for large deflections of a cantilever beam

A load case study of geometric nonlinear large deflections of a cantilever beam is presented. The bending strain must remain elastic. Closed form solution and finite element methods of analysis are illustrated and compared for three common load cases. A nondimensional nomogram for each case is presented in the summary.

Craig, L. D.↗

NASA NTRS1978

A Special Purpose Architecture for Finite Element Analysis

The analysis of aerospace structures by the finite element method consumes considerable computer time. The cost of this resource and the designer's desire to have rapid feedback concerning such questions as the effect of a change in loading of the structure or in a parameter of some structural material led to the design of a special purpose parallel computing system for finite element analysis. As a special purpose computer, the architecture of this finite element computer is closely tied to computational aspects of the particular problem. Various aspects of an MIMD array of microprocessors are related to the requirements of the class of finite element analysis problems which it is intended to solve.

Jordan, H. F.↗

NASA NTRS1984

Penalty function finite element analysis of steady viscous incompressible flow in rotating coordinates

Finite element methods for incompressible viscous flow in turbomachines have not been presented in the literature previously. This paper develops a penalty function primitive variable method including Coriolis and centrifugal force terms for steady flow in a rotating coordinate system. Simplex elements are used with the result of solution times comparable to equivalent finite different solutions. Example cases considered are Couette flow, Poiseuile flow, flow over a step and flow in a rotating channel. Both laminar and turbulent flows are discussed. The accuracy of computed solutions compares well with theoretical solutions and experimenal measurements.

Rosen, M. C.↗

NASA NTRS1985

Dynamic fracture mechanics

Dynamic fracture and crack propagation concepts for ductile materials are reviewed. The equations for calculating dynamic stress integrity and the dynamic energy release rate in order to study dynamic crack propagation are provided. The stress intensity factor versus crack velocity relation is investigated. The uses of optical experimental techniques and finite element methods for fracture analyses are described. The fracture criteria for a rapidly propagating crack under mixed mode conditions are discussed; crack extension and fracture criteria under combined tension and shear loading are based on maximum circumferential stress or energy criteria such as strain energy density. The development and use of a Dugdale model and finite element models to represent crack and fracture dynamics are examined.

Kobayashi, A. S.↗

NASA NTRS1994

Discretized energy minimization in a wave guide with point sources

An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.

Propst, G.↗

NASA NTRS1993

A Hybrid Symmetric FEM/MOM Formulation Applied to Scattering by Inhomogeneous Bodies of Revolution

A new symmetric formulation of the Hybrid Finite Element Method (HFEM) is described which combines elements of the Electric Field Integral Equation (EFIE) and the Magnetic Field Integral Equation (MFIE) for the exterior region along with the finite element solution for the interior problem. The formulation is applied to scattering by inhomogeneous bodies of revolution. To avoid spurious modes in the interior region a combination of vector and nodal based finite elements are used. Integral equations in the exterior region are used to enforce the Sommerfield radiation condition by matching both the tangential electric and magnetic fields between interior and exterior regions.

Lee, J-F.↗

NASA NTRS1991

Probabilistic Structural Analysis Methods (PSAM) for select space propulsion system components

This annual report summarizes the work completed during the third year of technical effort on the referenced contract. Principal developments continue to focus on the Probabilistic Finite Element Method (PFEM) which has been under development for three years. Essentially all of the linear capabilities within the PFEM code are in place. Major progress in the application or verifications phase was achieved. An EXPERT module architecture was designed and partially implemented. EXPERT is a user interface module which incorporates an expert system shell for the implementation of a rule-based interface utilizing the experience and expertise of the user community. The Fast Probability Integration (FPI) Algorithm continues to demonstrate outstanding performance characteristics for the integration of probability density functions for multiple variables. Additionally, an enhanced Monte Carlo simulation algorithm was developed and demonstrated for a variety of numerical strategies.

Source record↗

NASA NTRS1993

High temperature composite analyzer (HITCAN) user's manual, version 1.0

This manual describes 'how-to-use' the computer code, HITCAN (HIgh Temperature Composite ANalyzer). HITCAN is a general purpose computer program for predicting nonlinear global structural and local stress-strain response of arbitrarily oriented, multilayered high temperature metal matrix composite structures. This code combines composite mechanics and laminate theory with an internal data base for material properties of the constituents (matrix, fiber and interphase). The thermo-mechanical properties of the constituents are considered to be nonlinearly dependent on several parameters including temperature, stress and stress rate. The computation procedure for the analysis of the composite structures uses the finite element method. HITCAN is written in FORTRAN 77 computer language and at present has been configured and executed on the NASA Lewis Research Center CRAY XMP and YMP computers. This manual describes HlTCAN's capabilities and limitations followed by input/execution/output descriptions and example problems. The input is described in detail including (1) geometry modeling, (2) types of finite elements, (3) types of analysis, (4) material data, (5) types of loading, (6) boundary conditions, (7) output control, (8) program options, and (9) data bank.

Lackney, J. J.↗

NASA NTRS2014

Strain Gage Load Calibration of the Wing Interface Fittings for the Adaptive Compliant Trailing Edge Flap Flight Test

The safety-of-flight parameters for the Adaptive Compliant Trailing Edge (ACTE) flap experiment require that flap-to-wing interface loads be sensed and monitored in real time to ensure that the structural load limits of the wing are not exceeded. This paper discusses the strain gage load calibration testing and load equation derivation methodology for the ACTE interface fittings. Both the left and right wing flap interfaces were monitored; each contained four uniquely designed and instrumented flap interface fittings. The interface hardware design and instrumentation layout are discussed. Twenty-one applied test load cases were developed using the predicted in-flight loads. Pre-test predictions of strain gage responses were produced using finite element method models of the interface fittings. Predicted and measured test strains are presented. A load testing rig and three hydraulic jacks were used to apply combinations of shear, bending, and axial loads to the interface fittings. Hardware deflections under load were measured using photogrammetry and transducers. Due to deflections in the interface fitting hardware and test rig, finite element model techniques were used to calculate the reaction loads throughout the applied load range, taking into account the elastically-deformed geometry. The primary load equations were selected based on multiple calibration metrics. An independent set of validation cases was used to validate each derived equation. The 2-sigma residual errors for the shear loads were less than eight percent of the full-scale calibration load; the 2-sigma residual errors for the bending moment loads were less than three percent of the full-scale calibration load. The derived load equations for shear, bending, and axial loads are presented, with the calculated errors for both the calibration cases and the independent validation load cases.

Miller, Eric J.↗

NASA NTRS1981

An adaptive, multi-level method for elliptic boundary value problems

Subroutine PLTMG is a FORTRAN program for solving self-adjoint elliptic boundary value problems in general regions of R-squared. It is based on a piecewise linear triangle finite element method, an adaptive grid refinement procedure, and a multi-level iterative method to solve the resulting sets of linear equations. This paper describes the method and presents some numerical results and comparisons.

Bank, R. E.↗

NASA NTRS1978

Trends and techniques for space base electronics

A system was developed for depositing aluminum and aluminum alloys by the D.C. sputtering technique. This system which was designed for a high level of cleanliness and ion monitoring the deposition parameters during film preparation is ready for studying the deposition and annealing parameters upon double level metal preparation. The finite element method was studied for use in the computer modeling of two dimensional MOS transistor structures. An algorithm was developed for implementing a computer study which is based upon the finite difference method. The program was modified and used to calculate redistribution data for boron and phosphorous which had been predeposited by ion implantation with range and straggle conditions typical of those used at MSFC. Data were generated for 111 oriented SOS films with redistribution in N2, dry O2 and steam ambients. Data are given showing both two dimensional effects and the evolution of the junction depth, sheet resistance and integrated dose with redistribution time.

Gassaway, J. D.↗