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NASA NTRS1994

Transverse shear stresses and their sensitivity coefficients in multilayered composite panels

A computational procedure is presented for the accurate determination of transverse shear stresses and their sensitivity coefficients in flat multilayered composite panels subjected to mechanical and thermal loads. The sensitivity coefficients measure the sensitivity of the transverse shear stresses to variations in the different lamination and material parameters of the panel. The panel is discretized by using either a three-field mixed finite element model based on a two-dimensional first- order shear deformation plate theory or a two-field degenerate solid element with each of the displacement components having a linear variation throughout the thickness of the laminate. The evaluation of transverse shear stresses can be conveniently divided into two phases. The first phase consists of using a superconvergent recovery technique for evaluating the in-plane stresses in the different layers. In the second phase, the transverse shear stresses are evaluated by using piecewise integration, in the thickness direction, of the three-dimensional equilibrium equations. The same procedure is used for evaluating the sensitivity coefficients of the transverse shear stresses. The effectiveness of the computational procedure is demonstrated by means of numerical examples of multilayered cross-ply panels subjected to transverse loading, uniform temperature change, and uniform temperature gradient through the thickness of the panel. In each case the standard of the comparison is taken to be the exact solution of the three dimensional thermoelasticity equations of the panel.

Noor, Ahmed K.↗

NASA NTRS1982

Engine dynamic analysis with general nonlinear finite element codes. II - Bearing element implementation, overall numerical characteristics and benchmarking

Second-year efforts within a three-year study to develop and extend finite element (FE) methodology to efficiently handle the transient/steady state response of rotor-bearing-stator structure associated with gas turbine engines are outlined. The two main areas aim at (1) implanting the squeeze film damper element into a general purpose FE code for testing and evaluation; and (2) determining the numerical characteristics of the FE-generated rotor-bearing-stator simulation scheme. The governing FE field equations are set out and the solution methodology is presented. The choice of ADINA as the general-purpose FE code is explained, and the numerical operational characteristics of the direct integration approach of FE-generated rotor-bearing-stator simulations is determined, including benchmarking, comparison of explicit vs. implicit methodologies of direct integration, and demonstration problems.

Padovan, J.↗

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 NTRS1989

Global sensitivity analysis in control-augmented structural synthesis

In this paper, an integrated approach to structural/control design is proposed in which variables in both the passive (structural) and active (control) disciplines of an optimization process are changed simultaneously. The global sensitivity equation (GSE) method of Sobieszczanski-Sobieski (1988) is used to obtain the behavior sensitivity derivatives necessary for the linear approximations used in the parallel multidisciplinary synthesis problem. The GSE allows for the decoupling of large systems into smaller subsystems and thus makes it possible to determine the local sensitivities of each subsystem's outputs to its inputs and parameters. The advantages in using the GSE method are demonstrated using a finite-element representation of a truss structure equipped with active lateral displacement controllers, which is undergoing forced vibration.

Bloebaum, Christina L.↗

NASA NTRS1995

Progress in Integrated Fluid/Structure/Controls Computations Using High Fidelity Equations

Aeroelasticity that involves strong coupling of fluids, structures and controls is an important element in designing an aircraft. Computational aeroelasticity using low fidelity methods such as the linear aerodynamic flow equations coupled with the modal structural equations are well advanced. Though these low fidelity approaches are computationally less intensive, they are not adequate for the analysis of aircraft which can experience complex flow/structure interactions. Supersonic transports can experience vortex induced aeroelastic oscillations whereas subsonic transports can experience transonic buffet associated structural oscillations. Both aircraft may experience a dip in the flutter speed at the transonic regime. For accurate aeroelastic computations at these complex fluid/structure interaction situations, high fidelity equations such as the Navier-Stokes for fluids and the finite-elements for structures are needed. Using these high fidelity methods, design quantities such as structural stresses can be directly computed. Computations using these high fidelity equations require state-of-the-art large computational resources. This paper will describe the transition from potential equations to Euler/Navier-Stokes equations for fluids and from modal equations to finite element equations for structures. Complexities associated with grids for moving control surfaces will be discussed. All contents of the paper will be limited to those already presented at domestic conferences within U.S. such as those sponsored by AIAA. It will not include any materials related to HPCCP computational work.

Guruswamy, Guru P.↗

NASA NTRS2007

Compatibility Condition in Theory of Solid Mechanics (Elasticity, Structures, and Design Optimization)

The strain formulation in elasticity and the compatibility condition in structural mechanics have neither been understood nor have they been utilized. This shortcoming prevented the formulation of a direct method to calculate stress. We have researched and understood the compatibility condition for linear problems in elasticity and in finite element analysis. This has lead to the completion of the method of force with stress (or stress resultant) as the primary unknown. The method in elasticity is referred to as the completed Beltrami-Michell formulation (CBMF), and it is the integrated force method (IFM) in structures. The dual integrated force method (IFMD) with displacement as the primary unknown has been formulated. IFM and IFMD produce identical responses. The variational derivation of the CBMF yielded the new boundary compatibility conditions. The CBMF can be used to solve stress, displacement, and mixed boundary value problems. The IFM in structures produced high-fidelity response even with a modest finite element model. The IFM has influenced structural design considerably. A fully utilized design method for strength and stiffness limitation has been developed. The singularity condition in optimization has been identified. The CBMF and IFM tensorial approaches are robust formulations because of simultaneous emphasis on the equilibrium equation and the compatibility condition.

Patnaik, Surya N.↗

NASA NTRS1981

Blade loss transient dynamics analysis, volume 2. Task 2: Theoretical and analytical development. Task 3: Experimental verification

The component element method was used to develop a transient dynamic analysis computer program which is essentially based on modal synthesis combined with a central, finite difference, numerical integration scheme. The methodology leads to a modular or building-block technique that is amenable to computer programming. To verify the analytical method, turbine engine transient response analysis (TETRA), was applied to two blade-out test vehicles that had been previously instrumented and tested. Comparison of the time dependent test data with those predicted by TETRA led to recommendations for refinement or extension of the analytical method to improve its accuracy and overcome its shortcomings. The development of working equations, their discretization, numerical solution scheme, the modular concept of engine modelling, the program logical structure and some illustrated results are discussed. The blade-loss test vehicles (rig full engine), the type of measured data, and the engine structural model are described.

Gallardo, V. C.↗

NASA NTRS1984

Transition to turbulence in plane channel flows

Results obtained from a numerical simulation of the final stages of transition to turbulence in plane channel flow are described. Three dimensional, incompressible Navier-Stokes equations are numerically integrated to obtain the time evolution of two and three dimensional finite amplitude disturbances. Computations are performed on CYBER-203 vector processor for a 32x51x32 grid. Results are presented for no-slip boundary conditions at the solid walls as well as for periodic suction blowing to simulate active control of transition by mass transfer. Solutions indicate that the method is capable of simulating the complex character of vorticity dynamics during the various stages of transition and final breakdown. In particular, evidence points to the formation of a lambda-shape vortex and the subsequent system of horseshoe vortices inclined to the main flow direction as the main elements of transition. Calculations involving periodic suction-blowing indicate that interference with a wave of suitable phase and amplitude reduces the disturbance growth rates.

Biringen, S.↗

NASA NTRS2020

Solution of the Nonlinear High-Fidelity Generalized Method of Cells Micromechanics Relations via Order-Reduction Techniques

The High-Fidelity Generalized Method of Cells (HFGMC) is one technique, distinct from traditional finite element approaches, for accurately simulating nonlinear composite material behavior. In this work, the HFGMC global system of equations for doubly-periodic repeating unit cells with nonlinear constituents has been reduced in size through the novel application of a Petrov-Galerkin Proper Orthogonal Decomposition order-reduction scheme in order to improve its computational efficiency. Order-reduced models of an E-glass/Nylon 12 composite led to a 4.8 to 6.3x speedup in the equation assembly/solution runtime while maintaining model accuracy. This corresponded to a 21 to 38 percent reduction in total runtime. The significant difference in assembly/solution and total runtimes was attributed to the evaluation of integration point inelastic field quantities; this step was identical between the unreduced and order-reduced models. Nonetheless, order-reduced techniques offer the potential to significantly improve the computational efficiency of multiscale calculations.

Ricks, Trenton M.↗

NASA NTRS2006

STRANAL-PMC Version 2.0

Version 2.0 of the Strain Rate Dependent Analysis of Polymer Matrix Composites (STRANAL-PMC) software has been released. A prior version was reported in Analyzing Loads and Strains in Polymer- Matrix Composites (LEW-17227), NASA Tech Briefs, Vol. 26, No. 11 (November 2002), page 36. To recapitulate: Modified versions of constitutive equations of viscoplasticity of metals are used to represent deformation of a polymeric matrix. The equations are applied in a micromechanical approach, proceeding upward from slices of unit cells, through the ply level, to the laminate level. The constitutive equations are integrated in time by a Runge- Kutta technique. To predict the ultimate strength of each composite ply, failure criteria are implemented within the micromechanics. The inputs to STRANAL-PMC are the laminate geometry, properties of the fiber and matrix materials, and applied stress or strain versus time. The outputs are time-dependent stresses and strains at the slice, ply, and laminate levels. The improvements in version 2.0 include more rigorous representation of hydrostatic- stress effects in the matrix, refinement and extension of ply failure models, and capabilities to analyze transverse shear stresses. Version 2.0 can be implemented as a material-model code within transient dynamic finite-element codes.

Goldberg, Robert↗

NASA NTRS2003

Finite-Element Methods for Real-Time Simulation of Surgery

Two finite-element methods have been developed for mathematical modeling of the time-dependent behaviors of deformable objects and, more specifically, the mechanical responses of soft tissues and organs in contact with surgical tools. These methods may afford the computational efficiency needed to satisfy the requirement to obtain computational results in real time for simulating surgical procedures as described in Simulation System for Training in Laparoscopic Surgery (NPO-21192) on page 31 in this issue of NASA Tech Briefs. Simulation of the behavior of soft tissue in real time is a challenging problem because of the complexity of soft-tissue mechanics. The responses of soft tissues are characterized by nonlinearities and by spatial inhomogeneities and rate and time dependences of material properties. Finite-element methods seem promising for integrating these characteristics of tissues into computational models of organs, but they demand much central-processing-unit (CPU) time and memory, and the demand increases with the number of nodes and degrees of freedom in a given finite-element model. Hence, as finite-element models become more realistic, it becomes more difficult to compute solutions in real time. In both of the present methods, one uses approximate mathematical models trading some accuracy for computational efficiency and thereby increasing the feasibility of attaining real-time up36 NASA Tech Briefs, October 2003 date rates. The first of these methods is based on modal analysis. In this method, one reduces the number of differential equations by selecting only the most significant vibration modes of an object (typically, a suitable number of the lowest-frequency modes) for computing deformations of the object in response to applied forces.

Basdogan, Cagatay↗

NASA NTRS1983

Transition to turbulence in plane channel flow

A numerical simulation of the final stages of transition to turbulence in plane channel flow is reported. Three dimensional, incompressible Navier-Stokes equations are numerically integrated to obtain the time-evolution of two and three dimensional finite amplitude disturbances. Computations are performed on the CYBER-203 vector processor for a 32x51x32 grid. Results are presented for no-slip boundary conditions at the solid walls as well as for periodic suction-blowing to simulate active control of transition by mass transfer. Solutions indicate that the method is capable of simulating the complex character of vorticity dynamics during the various stages of transition and final breakdown. In particular, evidence points to the formation of a lambda-shape vortex and the subsequent system of horseshoe vortices inclined to the main flow direction as the main elements of transition. Calculations involving suction-blowing indicate that interference with a wave of suitable phase and amplitude reduces the disturbance growth rates.

Biringen, S.↗

NASA NTRS1988

A stiffly-stable implicit Runge-Kutta algorithm for CFD applications

A stiffly-stable implicit Runge-Kutta integration algorithm is derived for CFD applications spanning the range of semidiscrete theories. The algorithm family contains the one-step 'theta' algorithms, including backwards Euler and the trapezoidal rule, and provides a versatile framework to identify expressions governing algorithm stability characteristics. Parameters of a Runge-Kutta optimal implicit algorithm, second-order accurate in time and stiffly-stable, are established. This algorithm is implemented within a weak statement finite element semidiscrete formulation for one- and two-dimensional conservation law systems. Numerical results are compared to theta-algorithm solutions, for unsteady quasi-one-dimensional Euler predictions with shocks, and for a specially derived two-dimensional conservation law system modeling the Euler equations.

Baker, A. J.↗

NASA NTRS2004

Three-Dimensional High-Order Spectral Volume Method for Solving Maxwell's Equations on Unstructured Grids

A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of the Maxwell equations. All numerical procedures for outer boundary, material interface, zonal interface, and interior SV face are unified with a single characteristic formulation. The load balancing in a massive parallel computing environment is therefore easier to achieve. A parameter is introduced in the Riemann solver to control the strength of the smoothing term. Important aspects of the data structure and its effects to communication and the optimum use of cache memory are discussed. Results will be presented for plane TE and TM waves incident on a perfectly conducting cylinder for up to fifth order of accuracy, and a plane wave incident on a perfectly conducting sphere for up to fourth order of accuracy. Comparisons are made with exact solutions for these cases.

Liu, Yen↗

NASA NTRSDate not supplied

LS-DYNA User-Defined Internal Ballistic Modeling

- LS-DYNA Explicit Finite Element Analysis software and CADPROG Internal Ballistic Analysis code are integrated as a single modeling tool to analyze pyro-mechanical devices. - Combining these two codes allows the ballistic calculations to be performed without modeling the propellant in an FEA mesh. At each LS-DYNA time step, CADPROG is analytically run using the kinematic data (stroke, velocity, chamber volume) fed back from the LS-DYNA simulation. Calculated pressure is then applied to a piston or any applicable surface mesh in LS-DYNA model interactively. -All external loads such as friction, damping loads, assisting/resisting loads, locking/unlocking loads are modeled in LS-DYNA and coupled with pressure loads from CADPROG to create a fully defined equation of motion -Both codes are written in Fortran 77. CADPROG is inserted in LS-DYNA source code as a user-defined subroutine and re-compiled to generate a custom executable.

pyrotechnics↗

NASA NTRS1985

On numerical integration and computer implementation of viscoplastic models

Due to the stringent design requirement for aerospace or nuclear structural components, considerable research interests have been generated on the development of constitutive models for representing the inelastic behavior of metals at elevated temperatures. In particular, a class of unified theories (or viscoplastic constitutive models) have been proposed to simulate material responses such as cyclic plasticity, rate sensitivity, creep deformations, strain hardening or softening, etc. This approach differs from the conventional creep and plasticity theory in that both the creep and plastic deformations are treated as unified time-dependent quantities. Although most of viscoplastic models give better material behavior representation, the associated constitutive differential equations have stiff regimes which present numerical difficulties in time-dependent analysis. In this connection, appropriate solution algorithm must be developed for viscoplastic analysis via finite element method.

Chang, T. Y.↗

NASA NTRSDate not supplied

LS-DYNA User-Defined Internal Ballistic Modeling

LS-DYNA Explicit Finite Element Analysis software and CADPROG Internal Ballistic Analysis code are integrated as a single modeling tool to analyze pyro-mechanical devices. Coupling these two codes allows the ballistic calculations to be performed without modeling the propellant in an FEA mesh. At each LS-DYNA time step, CADPROG is run analytically using the kinematic data (stroke, velocity, chamber volume) fed back from the LS-DYNA simulation. The calculated pressure is then applied to a piston or any applicable surface mesh in LS-DYNA model interactively. All external loads such as friction, damping loads, assisting/resisting loads, locking/unlocking loads are modeled in LS-DYNA and coupled with pressure loads from CADPROG to create a fully defined equation of motion Both codes are written in Fortran 77. CADPROG is integrated in the LS-DYNA source code as a user-defined subroutine and recompiled to generate a custom executable.

pyrotechnics↗

NASA NTRS1985

Analysis of a finite composite plate with smooth rigid pin

An elastic continuum method of analysis developed for a smooth rigid pin in a finite composite plate by using complex potentials that satisfy the governing orthotropic differential equation is presented. The plate is subjected to uniaxial loading and the nonlinear problems of partial contact in the pin-plate are studied. Three types of pin fits are examined: interference, push, and clearance. The problems of stresses due to pure interference, load contact behavior, and stresses variations are addressed. The effects of the rectangular geometry and the orthotropic property of the plate are demonstrated through numerical results. It is found that the use of large hole diameter/plate width ratios have deleterious effects and the use of interference has beneficial effects. The solutions obtained will help in the development of special finite elements for fastener joints. Finally, the boundary conditions on the finite outer boundaries are found to be satisfied by a successive integration technique.

Naidu, A. C. B.↗