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At least 163 records · Page 9

Integrating chemical kinetic rate equations by selective use of stiff and nonstiff methods

The effect of switching between nonstiff and stiff methods on the efficiency of algorithms for integrating chemical kinetic rate equations is presented. Different integration methods are tested by application of the packaged code LSODE to four practical combustion kinetics problems. The problems describe adiabatic, homogeneous gas-phase combustion reactions. It is shown that selective use of nonstiff and stiff methods in different regimes of a typical batch combustion problem is faster than the use of either method for the entire problem. The implications of this result to the development of fast integration techniques for combustion kinetic rate equations are discussed.

Radhakrishnan, K.↗

Implicit extensions of an explicit multirate Runge–Kutta scheme

In this work, we propose a new method that extends conservative explicit multirate methods to implicit explicit-multirate methods. We develop extensions of order one and two with different stability properties on the implicit side. The method is suitable for time-stepping adaptive mesh refinement PDE discretizations with different degrees of stiffness. A numerical example with an advection-diffusion problem illustrates the new method's properties.

97 MATHEMATICS AND COMPUTING↗

The crack-inclusion interaction problem

The general plane elastostatic problem of interaction between a crack and an inclusion is considered. The Green's functions for a pair of dislocations and a pair of concentrated body forces are used to generate the crack and the inclusion. Integral equations are obtained for a line crack and an elastic line inclusion having an arbitrary relative orientation and size. The nature of stress singularity around the end points of rigid and elastic inclusions is described and three special cases of this intersection problem are studied. The problem is solved for an arbitrary uniform stress state away from the crack-inclusion region. The nonintersecting crack-inclusion problem is considered for various relative size, orientation, and stiffness parameters, and the stress intensity factors at the ends of the inclusion and the crack are calculated. For the crack-inclusion intersection case, special stress intensity factors are defined and are calculated for various values of the parameters defining the relative size and orientation of the crack and the inclusion and the stiffness of the inclusion.

Xue-Hui, L.↗

The crack-inclusion interaction problem

The general plane elastostatic problem of interaction between a crack and an inclusion is considered. The Green's functions for a pair of dislocations and a pair of concentrated body forces are used to generate the crack and the inclusion. Integral equations are obtained for a line crack and an elastic line inclusion having an arbitrary relative orientation and size. The nature of stress singularity around the end points of rigid and elastic inclusions is described and three special cases of this intersection problem are studied. The problem is solved for an arbitrary uniform stress state away from the crack-inclusion region. The nonintersecting crack-inclusion problem is considered for various relative size, orientation, and stiffness parameters, and the stress intensity factors at the ends of the inclusion and the crack are calculated. For the crack-inclusion intersection case, special stress intensity factors are defined and are calculated for various values of the parameters defining the relative size and orientation of the crack and the inclusion and the stiffness of the inclusion.

Liu, X.-H.↗

Active control of bearing preload using piezoelectric translators

In many spacecraft applications, mechanisms are required to perform precision pointing operations or to sometimes dither about or track a moving object. These mechanisms perform in a predictable and repeatable manner in benign temperature environments. Severe thermal gradients experienced in actual space applications however, cause assemblies to expand and contract around their bearings. This results in unpredictable changes in bearing preload, and hence bearing friction. This becomes a limitation for servos controlling pointing accuracy. Likewise, uncontrollable vibrations may couple into fixed preload (hence, fixed stiffness) mechanisms and limit pointing accuracy. Consequently, a complex problem faced today is how to design mechanisms that remain insensitive to changing thermal and vibrational spacecraft environments. Research presented involves the simplified modeling and test results of an actuator module that used piezoelectrically preload controlled bearings. The feasibility of actively controlling bearing preload was demonstrated. Because bearing friction is related to preload, a thermally active system designed with aluminum components and a 440 C bearing, was friction tested at temperatures ranging from 0 to 70 C (32 to 158 F). Effectiveness of the translators were demonstrated by mapping a controllable friction range throughout tested temperatures. It was learned that constant preload for this system could be maintained over an approximate 44 C (79 F) temperature span. From testing, it was also discovered that at the more deviate temperatures, expansions were so large that radial clearances were taken up and the duplex bearing became radially preloaded. Thus, active control of bearing preload is feasible but may be limited by inherent geometry constraints and materials used in the system.

Nye, Ted W.↗

Numerical recovery of material parameters in Euler-Bernoulli beam models

A fully Sinc-Galerkin method for recovering the spatially varying stiffness parameter in fourth-order time-dependence problems with fixed and cantilever boundary conditions is presented. The forward problems are discretized with a sinc basis in both the spatial and temporal domains. This yields an approximation solution which converges exponentially and is valid on the infinite time interval. When the forward methods are applied to parameter recovery problems, the resulting inverse problems are ill-posed. Tikhonov regularization is applied and the resulting minimization problems are solved via a quasi-Newton/trust region algorithm. The L-curve method is used to determine an appropriate value of the regularization parameter. Numerical results which highlight the method are given for problems with both fixed and cantilever boundary conditions.

Smith, R. C.↗

Active damping application to the shuttle RMS

Control Structure Interaction (CSI) is a relatively new technology developed over the last 10 to 15 years for application to large flexible space vehicles. The central issue is recognition that high performance control systems necessary for good spacecraft performance may adversely interact with the dynamics of the spacecraft structures, a problem increasingly aggravated by the large size and reduced stiffness of modern spacecraft structural designs. The CSI analysis and design methods were developed to avoid interactions while maintaining spacecraft performance without exceeding structural capabilities, but they remain largely unvalidated by hardware experiments or demonstrations, particularly in-space flight demonstrations. One recent proposal for a low cost flight validation of CSI technology is to demonstrate active damping augmentation of the Space Shuttle Remote Manipulator System (RMS). An analytical effort to define the potential for such an active damping augmentation demonstration to improve the structural dynamic response of the RMS following payload maneuvers is described. It is hoped that this study will lead to an actual inflight CSI test with the RMS using existing shuttle hardware to the maximum extent possible. By using the existing hardware, the flight demonstration results may eventually be of direct benefit to actual Space Shuttle RMS operations, especially during the construction of the Space Station Freedom.

Gilbert, Michael G.↗

Inclusion of transverse shear deformation in exact buckling and vibration analysis of composite plate assemblies

The problem considered is the development of the necessary plate stiffnesses for use in a general purpose program for buckling and vibration of composite plate assemblies. The required stiffnesses are for the assumption of sinusoidal response along the plate length with transverse shear included. The method is based on the exact solution of the plate differential equations for a composite laminate having fully populated A, B, and D matrices which leads to a differential equation of tenth order.

Anderson, Melvin S.↗

Inclusion of transverse shear deformation in the exact buckling and vibration analysis of composite plate assemblies

The problem considered is the development of the necessary plate stiffnesses for use in the general purpose program VICONOPT for buckling and vibration of composite plate assemblies. The required stiffnesses include the effects of transverse shear deformation and are for sinusoidal response along the plate length as required in VICONOPT. The method is based on the exact solution of the plate differential equations for a composite laminate having fully populated A, B, and D stiffness matrices which leads to an ordinary differential equation of tenth order.

Anderson, Melvin S.↗

Principles of moment distribution applied to stability of structures composed of bars or plates

The principles of the cross method of moment distribution, which have previously been applied to the stability of structures composed of bars under axial load, are applied to the stability of structures composed of long plates under longitudinal load. A brief theoretical treatment of the subject, as applied to structures composed of either bars or plates, is included, together with an illustrative example for each of these two types of structure. An appendix presents the derivation of the formulas for the various stiffnesses and carry-over factors used in solving problems in the stability of structures composed of long plates.

Lundquist, Eugene E↗

Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems

The ability of computers to solve hitherto intractable problems and simulate complex processes using mathematical models makes them an indispensable part of modern science and engineering. Computer simulations of large-scale realistic applications usually require solving a set of non-linear partial differential equations (PDES) over a finite region. For example, one thrust area in the DOE Grand Challenge projects is to design future accelerators such as the SpaHation Neutron Source (SNS). Our colleagues at SLAC need to model complex RFQ cavities with large aspect ratios. Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency. The PDEs for electromagnetics are discretized by the FEM method, which leads to a generalized eigenvalue problem Kx = AMx, where K and M are the stiffness and mass matrices, and are very sparse. In a typical cavity model, the number of degrees of freedom is about one million. For such large eigenproblems, direct solution techniques quickly reach the memory limits. Instead, the most widely-used methods are Krylov subspace methods, such as Lanczos or Jacobi-Davidson. In all the Krylov-based algorithms, sparse matrix-vector multiplication (SPMV) must be performed repeatedly. Therefore, the efficiency of SPMV usually determines the eigensolver speed. SPMV is also one of the most heavily used kernels in large-scale numerical simulations.

Oliker, Leonid↗

New displacement-based methods for optimal truss topology design

Two alternate methods for maximum stiffness truss topology design are presented. The ground structure approach is used, and the problem is formulated in terms of displacements and bar areas. This large, nonconvex optimization problem can be solved by a simultaneous analysis and design approach. Alternatively, an equivalent, unconstrained, and convex problem in the displacements only can be formulated, and this problem can be solved by a nonsmooth, steepest descent algorithm. In both methods, the explicit solving of the equilibrium equations and the assembly of the global stiffness matrix are circumvented. A large number of examples have been studied, showing the attractive features of topology design as well as exposing interesting features of optimal topologies.

Bendsoe, Martin P.↗

An approach to probabilistic finite element analysis using a mixed-iterative formulation

An efficient algorithm for computing the response sensitivity of finite element problems based on a mixed-iterative formulation is proposed. This method does not involve explicit differentiation of the tangent stiffness array and can be used with formulations for which a consistent tangent stiffness is not readily available. The method has been successfully applied to probabilistic finite element analysis of problems using the proposed mixed formulation, and this exercise has provided valuable insights regarding the extension of the method to a more general class of problems to include material and geometric nonlinearities.

Dias, J. B.↗

Cantilever Wings for Modern Aircraft: Some Aspects of Cantilever Wing Construction with Special Reference to Weight and Torsional Stiffness

In the foregoing remarks I have made an attempt to touch on some of the structural problems met with in cantilever wings, and dealt rather fully with a certain type of single-spar construction. The experimental test wing was a first attempt to demonstrate the principles of this departure from orthodox methods. The result was a wing both torsionally stiff and of light weight - lighter than a corresponding biplane construction.

WINGS - STRUCTURE↗

A Lanczos eigenvalue method on a parallel computer

Eigenvalue analyses of complex structures is a computationally intensive task which can benefit significantly from new and impending parallel computers. This study reports on a parallel computer implementation of the Lanczos method for free vibration analysis. The approach used here subdivides the major Lanczos calculation tasks into subtasks and introduces parallelism down to the subtask levels such as matrix decomposition and forward/backward substitution. The method was implemented on a commercial parallel computer and results were obtained for a long flexible space structure. While parallel computing efficiency for the Lanczos method was good for a moderate number of processors for the test problem, the greatest reduction in time was realized for the decomposition of the stiffness matrix, a calculation which took 70 percent of the time in the sequential program and which took 25 percent of the time on eight processors. For a sample calculation of the twenty lowest frequencies of a 486 degree of freedom problem, the total sequential computing time was reduced by almost a factor of ten using 16 processors.

Bostic, Susan W.↗

A Lanczos eigenvalue method on a parallel computer

Eigenvalue analyses of complex structures is a computationally intensive task which can benefit significantly from new and impending parallel computers. This study reports on a parallel computer implementation of the Lanczos method for free vibration analysis. The approach used here subdivides the major Lanczos calculation tasks into subtasks and introduces parallelism down to the subtask levels such as matrix decomposition and forward/backward substitution. The method was implemented on a commercial parallel computer and results were obtained for a long flexible space structure. While parallel computing efficiency is problem and computer dependent, the efficiency for the Lanczos method was good for a moderate number of processors for the test problem. The greatest reduction in time was realized for the decomposition of the stiffness matrix, a calculation which took 70 percent of the time in the sequential program and which took 25 percent of the time on eight processors. For a sample calculation of the twenty lowest frequencies of a 486 degree of freedom problem, the total sequential computing time was reduced by almost a factor of ten using 16 processors.

Bostic, Susan W.↗