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NASA NTRS1987

Mechanics of materials model

The Mechanics of Materials Model (MOMM) is a three-dimensional inelastic structural analysis code for use as an early design stage tool for hot section components. MOMM is a stiffness method finite element code that uses a network of beams to characterize component behavior. The MOMM contains three material models to account for inelastic material behavior. These include the simplified material model, which assumes a bilinear stress-strain response; the state-of-the-art model, which utilizes the classical elastic-plastic-creep strain decomposition; and Walker's viscoplastic model, which accounts for the interaction between creep and plasticity that occurs under cyclic loading conditions.

Meister, Jeffrey P.↗

NASA NTRS1989

Integrated design optimization research and development in an industrial environment

An overview is given of a design optimization project that is in progress at the GE Research and Development Center for the past few years. The objective of this project is to develop a methodology and a software system for design automation and optimization of structural/mechanical components and systems. The effort focuses on research and development issues and also on optimization applications that can be related to real-life industrial design problems. The overall technical approach is based on integration of numerical optimization techniques, finite element methods, CAE and software engineering, and artificial intelligence/expert systems (AI/ES) concepts. The role of each of these engineering technologies in the development of a unified design methodology is illustrated. A software system DESIGN-OPT has been developed for both size and shape optimization of structural components subjected to static as well as dynamic loadings. By integrating this software with an automatic mesh generator, a geometric modeler and an attribute specification computer code, a software module SHAPE-OPT has been developed for shape optimization. Details of these software packages together with their applications to some 2- and 3-dimensional design problems are described.

Kumar, V.↗

NASA NTRS1989

Finite element flow-thermal-structural analysis of aerodynamically heated leading edges

Hypersonic vehicles operate in a hostile aerothermal environment which has a significant impact on their aerothermostructural performance. Significant coupling occurs between the aerodynamic flow field, structural heat transfer, and structural response creating a multidisciplinary interaction. A long term goal of the Aerothermal Loads Branch at the NASA Langley Research Center is to develop a computational capability for integrated fluid, thermal and structural analysis of aerodynamically heated structures. The integrated analysis capability includes the coupling between the fluid and the structure which occurs primarily through the thermal response of the structure, because: (1) the surface temperature affects the external flow by changing the amount of energy absorbed by the structure, and (2) the temperature gradients in the structure result in structural deformations which alter the flow field and attendant surface pressures and heating rates. In the integrated analysis, a finite element method is used to solve: (1) the Navier-Stokes equations for the flow solution, (2) the energy equation of the structure for the temperature response, and (3) the equilibrium equations of the structure for the structural deformation and stresses.

Dechaumphai, Pramote↗

NASA NTRS1989

Shear buckling of specially orthotropic plates with centrally located cutouts

The shear loading of a composite rectangular plate with a centrally located circular cutout was analyzed in order to predict the buckling load of the plate. The first step in this analysis is to calculare the in-plane stress distribution of the plate prior to buckling. This problem can be solved using finite element methods, but a quicker and more cost efficient method is desired. The method chosen to determine the pre-buckling stresses is that of boundary collocation using complex variables. The real valued force functions are written in terms of two complex valued functions, each of which is a function of a different complex variable. The solution of the generalized biharmonic function is a superposition of functions of these two complex variables. For this analysis, the force functions are represented with a Laurent series. The constants in these series are found using boundary collocation. Two force equations for complex variables are satisfied over the plate boundaries to obtain these constants. The stresses in the plate are then known for any particular locations on the plate given the applied shear on the edges of the plate.

Klang, Eric C.↗

NASA NTRS1989

Environmental concept for engineering software on MIMD computers

The issues related to developing an environment in which engineering systems can be implemented on MIMD machines are discussed. The problem is presented in terms of implementing the finite element method under such an environment. However, neither the concepts nor the prototype implementation environment are limited to this application. The topics discussed include: the ability to schedule and synchronize tasks efficiently; granularity of tasks; load balancing; and the use of a high level language to specify parallel constructs, manage data, and achieve portability. The objective of developing a virtual machine concept which incorporates solutions to the above issues leads to a design that can be mapped onto loosely coupled, tightly coupled, and hybrid systems.

Lopez, L. A.↗

NASA NTRS1989

Control of the errors of discretization and idealization in finite element analysis

Understanding of the basic principles which control errors of discretization in finite element analysis has increased very substantially since 1980. The main milestones were: (1) development of the theoretical basis of p-extensions (1981); (2) understanding of the proper interplay between mesh design and assignment of polynomial degree to elements. Practical realization of exponential convergence rates, independently of the smoothness of the exact solution (1984); and (3) industrial experience with the new finite element technology known as the p- or hp-version of the finite element method: General Dynamics reported thirty- to forty-fold savings in terms of human time and large savings in computer time (1986). Lockheed reported favorably on their evaluation of error estimation and quality control capabilities of the p-version in industrial settings (1987). The gains in our understanding of how to control the errors of discretization represent only half of the control necessary to ensure that a numerical model is in fact an accurate representation of the corresponding physical system. Control of the errors of idealization is equally important. A brief overview of the main ideas of how to ensure the quality and reliability of mathematical models of structural systems is presented.

Szabo, Barna A.↗

NASA NTRS1988

Factors influencing elastic stresses in double cantilever beam specimens

An elastic stress analysis was conducted for a double cantilever beam (DCB) specimen using finite-element methods. The purpose of this study was to identify the important parameters that influence stresses ahead of the delamination front. The study focused on an aluminum DCB specimen, typical of adhesively-bonded joints, and on a graphite/epoxy specimen representing a cocured composite. Opening mode sigma sub y stresses ahead of the crack tip were calculated and compared with those for a monolithic reference specimen. Beyond the singularity-dominated region very near the crack tip, the sigma sub y distribution was elevated compared to the monolithic case. Both the adhesive thickness and the adherend transverse (thickness-direction) stiffness were found to influence the elevation of sigma sub y. In contrast, adherend thickness and longitudinal stiffness has very little effect on this stress distribution. Estimates for adhesive yielding beyond the aluminum DCB crack tip showed that both the area and height of the plastic zone increased to a peak value for increasing adhesive thicknesses. Results from this study would provide insight for comparing data from different DCB specimens and for designing new DCB specimens.

Crews, J. H., Jr.↗

NASA NTRS1988

Resolved shear stress intensity coefficient and fatigue crack growth in large crystals

Fatigue crack growth tests were carried out on large-grain Al 7029 aluminum alloy and the finite element method was used to calculate the stress field near the tip of a zigzag crack. The resolved shear stresses on all 12 slip systems were computed, and the resolved shear stress intensity coefficient (RSSIC) was defined. The RSSIC was used to analyze the irregular crack path and was correlated with the rate of single-slip-plane shear crack growth. Fatigue crack growth was found to be caused primarily by shear decohesion at a crack tip. When the RSSIC on a single-slip system was much larger than all the others, the crack followed a single-slip plane. When the RSSICs on two conjugate slip systems were comparable, a crack grew in a zigzag manner on these planes and the macrocrack-plane bisected the two active slip planes. The maximum RSSIC on the most active slip system is proposed as a parameter to correlate with the shear fatigue crack growth rate in large crystals.

Chen, Q.↗

NASA NTRS1988

Kuhn-Tucker optimization based reliability analysis for probabilistic finite elements

The fusion of probability finite element method (PFEM) and reliability analysis for fracture mechanics is considered. Reliability analysis with specific application to fracture mechanics is presented, and computational procedures are discussed. Explicit expressions for the optimization procedure with regard to fracture mechanics are given. The results show the PFEM is a very powerful tool in determining the second-moment statistics. The method can determine the probability of failure or fracture subject to randomness in load, material properties and crack length, orientation, and location.

Liu, W. K.↗

NASA NTRS1989

Composite mechanics for engine structures

Recent research activities and accomplishments at Lewis Research Center on composite mechanics for engine structures are summarized. The activities focused mainly on developing procedures for the computational simulation of composite intrinsic and structural behavior. The computational simulation encompasses all aspects of composite mechanics, advanced three-dimensional finite-element methods, damage tolerance, composite structural and dynamic response, and structural tailoring and optimization.

Chamis, Christos C.↗

NASA NTRS1988

Strain energy release rate analysis of delamination in a tapered laminate subjected to tension load

Finite element method was used to analyze a tapered glass/epoxy composite laminate subjected to a tension load, in order to determine the interlaminar stress distributions the strain-energy release rate for the delamination growth that may occur due to ply drops. In a laminate having a typical configuration of a helicopter hub, the (+/- 45)3 plies were dropped in three distinct steps, each 20-ply thickness apart, with the resulting taper angle of 5.71 deg. Delaminations were assumed to initiate at the bottom of the taper on the -45/+45 interface, and the delamination growth was simulated along the taper and into the thin region. The results of the analysis indicated that a delamination initiating at the end of the taper will grow unstably along the taper and the thin laminate simultaneously.

Salpekar, S. A.↗

NASA NTRS1988

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

Mostrel, M. M.↗

NASA NTRS1989

Design of laminated plates for maximum buckling load

The buckling load of laminated plates having midplane symmetry is maximized for a given total thickness. The thicknesses of the layers are taken as the design variables. Buckling analysis is carried out using the finite element method. The optimality equations are solved by a homotopy method which permits tracing optima as a function of total thickness. It is shown that for any design with a given stacking sequence of ply orientations, there exists a design associated with any other stacking sequence which possesses the same bending stiffness matrix and same total thickness. Hence, from the optimum design for a given stacking sequence, one can directly determine the optimum design for any rearrangement of the ply orientations, and the optimum buckling load is independent of the stacking sequence.

Shin, Yung S.↗

NASA NTRS1989

Finite element computation of hypersonic flow past a complete body

The finite element method was applied to compressible flows past complete blunt bodies in a first attempt to use the method to model hypersonic flow past re-entry vehicles. A Runge-Kutta time marching scheme was utilized and was found to adequately handle the bow shock and downstream wake. Adaptive refinement was successively applied to the flow field grid, and improvement in solution accuracy was observed. The results reported in this paper include the flow past a circular cylinder at Mach 3, and the flow in the plane of symmetry for the flow past a sphere at Mach 10.

Hommel, Mark↗

NASA NTRS1989

Thermo-viscoelastic analysis of composite materials

The thermo-viscoelastic boundary value problem for anisotropic materials is formulated and a numerical procedure is developed for the efficient analysis of stress and deformation histories in composites. The procedure is based on the finite element method and therefore it is applicable to composite laminates containing geometric discontinuities and complicated boundary conditions. Using the present formulation, the time-dependent stress and strain distributions in both notched and unnotched graphite/epoxy composites have been obtained. The effect of temperature and ply orientation on the creep and relaxation response is also studied.

Lin, Kuen Y.↗

NASA NTRS1989

A package for unstructured grid generation and finite element flow solvers

A set of programs for unstructured mesh construction, fluid flow calculation and flow field visualization in two and three dimensions is described. The grid generators are based on the advancing front concept. The flow solvers use the finite element methods with Flux Corrected Transport techniques to solve several sets of equations including the Euler and Burger's equations. Several examples show the flexibility and accuracy of the methods.

Gumbert, Clyde↗

NASA NTRS1990

Dissipation Of Energy In Extension Of Cracks

Dissipation in elastic-plastic material calculated by two-dimensional finite-element method. Analytical procedure developed to calculate various components of dissipation of energy during extension of crack and to relate them to total dissipation of energy computed from global load-displacement response. Observations in study valid for other elastic-plastic fracture situations, including growth of cracks in pressure vessels in nuclear powerplants.

Shivakumar, Kunigal N.↗

NASA NTRS1990

Delamination Analysis Of Composite Curved Bars

Classical anisotropic elasticity theory used to construct "multilayer" composite semicircular curved bar subjected to end forces and end moments. Radial location and intensity of open-mode delamination stress calculated and compared with results obtained from anisotropic continuum theory and from finite element method. Multilayer theory gave more accurate predictions of location and intensity of open-mode delamination stress. Currently being applied to predict open-mode delamination stress concentrations in horse-shoe-shaped composite test coupons.

Ko, William L.↗