A Delta-Tracking Method That Supports Finite-Element Material Properties in Mesh-Based Monte Carlo Codes
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The Interpretation of Crustal Dynamics Data in Terms of Plate Interactions and Active Tectonics of the Anatolian Plate and Surrounding Regions in the Middle East
During the past 6 months, efforts were concentrated on the following areas: (1) Continued development of realistic, finite element modeling of plate interactions and associated deformation in the Eastern Mediterranean; (2) Neotectonic field investigations of seismic faulting along the active fault systems in Turkey with emphasis on identifying seismic gaps along the North Anatolian fault; and (3) Establishment of a GPS regional monitoring network in the zone of ongoing continental collision in eastern Turkey (supported in part by NSF).
Toksoz, M. Nafi↗
WARP3D-Release 10.8: Dynamic Nonlinear Analysis of Solids using a Preconditioned Conjugate Gradient Software Architecture
This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.
Koppenhoefer, Kyle C.↗
An iterative finite element-integral technique for predicting sound radiation from turbofan inlets in steady flight
A new iterative solution technique for predicting the sound field radiated from a turbofan inlet in steady flight is presented. The sound field is divided into two regions: the sound field within and near the inlet which is computed using the finite element method and the radiation field beyond the inlet which is calculated using an integral solution technique. A continuous solution is obtained by matching the finite element and integral solutions at the interface between the two regions. The applicability of the iterative technique is demonstrated by comparison of experimental results with the theoretical results for several different inlet configurations with and without flow. These examples show that good agreement between experiment and theory is obtained within five iterations.
Horowitz, S. J.↗
Optimization of acoustic liners by the hybrid finite element-integral approach
An iterative solution technique for predicting the sound field radiated from a turbofan inlet is used to predict the optimum inlet acoustic liner. The analytical approach divides the sound field into two regions: the sound field within and near the inlet which is computed using the finite element method and the radiation field beyond the inlet which is calculated using an integral solution technique. A continuous solution is obtained by matching the finite element and integral solutions at the interface between the two regions. Using a trial and error scheme, this analytical procedure is used to calculate the impedance value of the duct liner which will produce a minimum sound pressure level in the far field. Several examples of straight and non-uniform ducts with and without flow are presented.
Sigman, R. K.↗
A Novel Multiscale Physics Based Progressive Failure Methodology for Laminated Composite Structures
A variable fidelity, multiscale, physics based finite element procedure for predicting progressive damage and failure of laminated continuous fiber reinforced composites is introduced. At every integration point in a finite element model, progressive damage is accounted for at the lamina-level using thermodynamically based Schapery Theory. Separate failure criteria are applied at either the global-scale or the microscale in two different FEM models. A micromechanics model, the Generalized Method of Cells, is used to evaluate failure criteria at the micro-level. The stress-strain behavior and observed failure mechanisms are compared with experimental results for both models.
Pineda, Evan J.↗
Modelling of thick composites using a layerwise laminate theory
The layerwise laminate theory of Reddy (1987) is used to develop a layerwise, two-dimensional, displacement-based, finite element model of laminated composite plates that assumes a piecewise continuous distribution of the tranverse strains through the laminate thickness. The resulting layerwise finite element model is capable of computing interlaminar stresses and other localized effects with the same level of accuracy as a conventional 3D finite element model. Although the total number of degrees of freedom are comparable in both models, the layerwise model maintains a 2D-type data structure that provides several advantages over a conventional 3D finite element model, e.g. simplified input data, ease of mesh alteration, and faster element stiffness matrix formulation. Two sample problems are provided to illustrate the accuracy of the present model in computing interlaminar stresses for laminates in bending and extension.
Robbins, D. H., Jr.↗
Derivation and verification of the direct-sampling method for simulating Monte Carlo flight paths in tetrahedral meshes with linear finite-element cross sections
This paper provides a derivation of a direct-sampling approach for modeling continuously varying cross sections in tetrahedral-mesh-based Monte Carlo codes. Specifically, cross sections are spatially approximated using linear nodal finite elements. A linearization strategy is provided for non-linearly varying cross sections. The method is verified against seven analytical pure-absorber test problems. These test problems also highlight the benefit of using linear finite elements over element-wise-constant cross sections.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Influence of backup bearings and support structure dynamics on the behavior of rotors with active supports
Progress over the past year includes the following: A simplified rotor model with a flexible shaft and backup bearings has been developed. A simple rotor model which includes a flexible disk and bearings with clearance has been developed and the dynamics of the model investigated. A rotor model based upon the T-501 engine has been developed which includes backup bearing effects. Parallel simulation runs are being conducted using an ANSYS based finite element model of the T-501. The magnetic bearing test rig is currently floating and dynamics/control tests are being conducted. A paper has been written that documents the work using the T-501 engine model. Work has continued with the simplified model. The finite element model is currently being modified to include the effects of foundation dynamics. A literature search for material on foil bearings has been conducted. A finite element model is being developed for a magnetic bearing in series with a foil backup bearing.
Flowers, George T.↗
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.↗
Probabilistic Structural Analysis Methods (PSAM) for select space propulsion system components
The fourth year of technical developments on the Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) system for Probabilistic Structural Analysis Methods is summarized. The effort focused on the continued expansion of the Probabilistic Finite Element Method (PFEM) code, the implementation of the Probabilistic Boundary Element Method (PBEM), and the implementation of the Probabilistic Approximate Methods (PAppM) code. The principal focus for the PFEM code is the addition of a multilevel structural dynamics capability. The strategy includes probabilistic loads, treatment of material, geometry uncertainty, and full probabilistic variables. Enhancements are included for the Fast Probability Integration (FPI) algorithms and the addition of Monte Carlo simulation as an alternate. Work on the expert system and boundary element developments continues. The enhanced capability in the computer codes is validated by applications to a turbine blade and to an oxidizer duct.
Source record↗
Gyrokinetic electromagnetic particle simulations in triangular meshes with C1 finite elements
The triangular mesh-based gyrokinetic scheme enables comprehensive axis-to-edge studies across the entire plasma volume. Our approach employs triangular finite elements with first-derivative continuity (C1), building on previous work to facilitate gyrokinetic simulations. Additionally, we have adopted the mixed variable/pullback scheme for gyrokinetic electromagnetic particle simulations. The filter-free treatment in the poloidal cross-section with triangular meshes introduces unique features and challenges compared to previous treatments using structured meshes. Our implementation has been validated through benchmarks using ITPA-toroidicity-induced Alfvén eigenmode parameters, showing its capability in moderate to small electron skin depth regimes. Additional examinations using experimental parameters confirm its applicability to realistic plasma conditions.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Finite elements of nonlinear continua.
The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.
Oden, J. T.↗
An analytical investigation of shape control of large space structures by applied temperatures
An analytical procedure for the static shape control of flexible space structures subjected to thermal distortions is developed which is based on prescribing temperatures in control elements having much higher coefficients of thermal expansion than the main structure. The temperatures at the control elements are defined so as to minimize the overall thermal distortion of the structure from its ideal shape, and a matrix equation is obtained which can be solved for the set of optimum control temperatures. A formulation of the procedure for continuous structures governed by differential equations and a formulation for discrete (finite element modeled) structures governed by matrix equations are presented. The equations from the continuous formulation are employed for the shape control of a simple beam distorted by nonuniform heating, and the discrete formulation is applied in a general purpose finite-element structural analysis computer program for the shape control of a 750 m radiometer antenna reflector dish subjected to orbital heating. A reduction in thermal distortion by a factor of nearly 50 was obtained with the use of only seven control elements. Results for four different sets of control locations for the antenna are presented in which reductions in distortion of up to a factor of four were obtained.
Haftka, R. T.↗
Static and dynamic characteristics of large deployable space reflectors
A linear numerical model of the structural characteristics of deployable reflectors was developed. Due to cyclic symmetry of the reflector structure about its axis, only one of many segments is modeled using finite elements. The succeeding segments satisfy continuity of displacement and slope at the interface between consecutive segments. This process leads to (N/2+1) static or dynamic problems of smaller order and bandwidth where N is the number of segments. The solution of each reduced problem leads to motions having a distinct circumferential wave number. The dynamic coupling to the feed support structure is studied adopting modal synthesis.
El-Raheb, M.↗
Finite-element modeling of layered, anisotropic composite plates and shells: A review of recent research
Finite element papers published in the open literature on the static bending and free vibration of layered, anisotropic, and composite plates and shells are reviewed. A literature review of large-deflection bending and large-amplitude free oscillations of layered composite plates and shells is also presented. Non-finite element literature is cited for continuity of the discussion.
Reddy, J. N.↗
Error analysis and correction of discrete solutions from finite element codes
Many structures are an assembly of individual shell components. Therefore, results for stresses and deflections from finite element solutions for each shell component should agree with the equations of shell theory. This paper examines the problem of applying shell theory to the error analysis and the correction of finite element results. The general approach to error analysis and correction is discussed first. Relaxation methods are suggested as one approach to correcting finite element results for all or parts of shell structures. Next, the problem of error analysis of plate structures is examined in more detail. The method of successive approximations is adapted to take discrete finite element solutions and to generate continuous approximate solutions for postbuckled plates. Preliminary numerical results are included.
Thurston, G. A.↗
Superelement methods applications to micromechanics of high temperature metal matrix composites
Adaptation of the superelement finite-element method for micromechanics of continuous fiber high temperature metal matrix composites (HT-MMC) is described. The method is used to predict the thermomechanical behavior of P100-graphite/copper composites using MSC/NASTRAN and it is also used to validate those predicted by using an in-house computer program designed to perform micromechanics for HT-MMC. Typical results presented in the paper include unidirectional composite thermal properties, mechanical properties, and microstresses.
Caruso, J. J.↗