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Recent developments in two areas of structural sensitivity analysis are reviewed. These are the sensitivity of static and transient response, and the sensitivity of vibration and buckling eigenproblems. Recent developments from the point of view of computational cost, accuracy, and ease of implementation are considered.
Innovative techniques applicable to sensitivity analysis of discretized structural systems are reviewed. The techniques include a finite difference step size selection algorithm, a method for derivatives of iterative solutions, a Green's function technique for derivatives of transient response, simultaneous calculation of temperatures and their derivatives, derivatives with respect to shape, and derivatives of optimum designs with respect to problem parameters. Computerized implementations of sensitivity analysis and applications of sensitivity derivatives are also discussed. Some of the critical needs in the structural sensitivity area are indicated along with plans for dealing with some of those needs.
Some innovative techniques applicable to sensitivity analysis of discretized structural systems are reviewed. These techniques include a finite-difference step-size selection algorithm, a method for derivatives of iterative solutions, a Green's function technique for derivatives of transient response, a simultaneous calculation of temperatures and their derivatives, derivatives with respect to shape, and derivatives of optimum designs with respect to problem parameters. Computerized implementations of sensitivity analysis and applications of sensitivity derivatives are also discussed. Finally, some of the critical needs in the structural sensitivity area are indicated along with Langley plans for dealing with some of these needs.
Recent developments are reviewed in two major areas of structural sensitivity analysis: sensitivity of static and transient response; and sensitivity of vibration and buckling eigenproblems. Recent developments from the standpoint of computational cost, accuracy, and ease of implementation are presented. In the area of static response, current interest is focused on sensitivity to shape variation and sensitivity of nonlinear response. Two general approaches are used for computing sensitivities: differentiation of the continuum equations followed by discretization, and the reverse approach of discretization followed by differentiation. It is shown that the choice of methods has important accuracy and implementation implications. In the area of eigenproblem sensitivity, there is a great deal of interest and significant progress in sensitivity of problems with repeated eigenvalues. In addition to reviewing recent contributions in this area, the paper raises the issue of differentiability and continuity associated with the occurrence of repeated eigenvalues.
Mechanical model for dynamic buckling of elastic imperfection-sensitive structures under step loading, using perturbation method
The implementation of static and dynamic structural-sensitivity derivative calculations in a general purpose, finite-element computer program denoted the Engineering Analysis Language (EAL) System is described. Derivatives are calculated with respect to structural parameters, specifically, member sectional properties including thicknesses, cross-sectional areas, and moments of inertia. Derivatives are obtained for displacements, stresses, vibration frequencies and mode shapes, and buckling loads and mode shapes. Three methods for calculating derivatives are implemented (analytical, semianalytical, and finite differences), and comparisons of computer time and accuracy are made. Results are presented for four examples: a swept wing, a box beam, a stiffened cylinder with a cutout, and a space radiometer-antenna truss.
A black-box approach to static condensation for sensitivity analysis is presented with illustrative examples of a cube and a car structure. The sensitivity of the structural response with respect to joint stiffness parameter is calculated using the direct method, forward-difference, and central-difference schemes. The efficiency of the various methods for identifying joint stiffness parameters from measured static deflections of these structures is compared. The results indicate that the use of static condensation can reduce computation times significantly and the black-box approach is only slightly less efficient than the standard implementation of static condensation. The ease of implementation of the black-box approach recommends it for use with general-purpose finite element codes that do not have a built-in facility for static condensation.
Acceptance of new spacecraft structural architectures and concepts requires validated design methods to minimize the expense involved with technology validation via flighttesting. This paper explores the implementation of probabilistic methods in the sensitivity analysis of the structural response of a Hypersonic Inflatable Aerodynamic Decelerator (HIAD). HIAD architectures are attractive for spacecraft deceleration because they are lightweight, store compactly, and utilize the atmosphere to decelerate a spacecraft during re-entry. However, designers are hesitant to include these inflatable approaches for large payloads or spacecraft because of the lack of flight validation. In the example presented here, the structural parameters of an existing HIAD model have been varied to illustrate the design approach utilizing uncertainty-based methods. Surrogate models have been used to reduce computational expense several orders of magnitude. The suitability of the design is based on assessing variation in the resulting cone angle. The acceptable cone angle variation would rely on the aerodynamic requirements.
Plastic postbuckling and imperfection sensitivity of spherical shells under axisymmetric bifurcation
Axisymmetric plastic deformation of imperfection sensitive spherical shell after elastic buckling, considering load carrying capacity
Thin film formation, deposition methods and relation to film structure and properties
An objective of the High Performance Computing and Communication Program at the NASA Langley Research Center is to demonstrate multidisciplinary shape and sizing optimization of a complete aerospace vehicle configuration by using high-fidelity, finite-element structural analysis and computational fluid dynamics aerodynamic analysis. In a previous study, a multi-disciplinary analysis system for a high-speed civil transport was formulated to integrate a set of existing discipline analysis codes, some of them computationally intensive, This paper is an extension of the previous study, in which the sensitivity analysis for the coupled aerodynamic and structural analysis problem is formulated and implemented. Uncoupled stress sensitivities computed with a constant load vector in a commercial finite element analysis code are compared to coupled aeroelastic sensitivities computed by finite differences. The computational expense of these sensitivity calculation methods is discussed.
Wear experiments and electron microscopy and diffraction studies were conducted to examine the wear and deformed layers in single-crystal Mn-Zn (ceramic) ferrite magnetic head material in contact with magnetic tape and the effects of that contact on magnetic properties. The crystalline state of the single-crystal magnetic head was changed drastically during the sliding process. A nearly amorphous structure was produced on its wear surface. Deformation in the surficial layer of the magnetic head was a critical factor in readback signal loss above 2.5 dB. The signal output level was reduced as applied normal load was increased. Considerable plastic flow occurred on the magnetic tape surface with sliding, and the signal loss due to the tape wear was approximately 1 dB.
The paper discusses two uses of the semianalytical methods for nonlinear sensitivity analysis. First, the application to noncritical response is analyzed. It is shown that the semianalytical method is equivalent to a particular form of the overall finite difference approach. It is concluded that the difference between overall finite differences and the semianalytical approach is blurred for the case of nonlinear static response. Next, the application of the semianalytical method to calculating sensitivities of limit loads is discussed. A formulation that is easy to implement in general purpose finite element programs is derived. Three examples are used to demonstrate the application of the formulation and to explore its accuracy.
The methodology used to implement structural sensitivity calculations into a major, general-purpose finite-element analysis system (SPAR) is described. This implementation includes a generalized method for specifying element cross-sectional dimensions as design variables that can be used in analytically calculating derivatives of output quantities from static stress, vibration, and buckling analyses for both membrane and bending elements. Limited sample results for static displacements and stresses are presented to indicate the advantages of analytically calculating response derivatives compared to finite difference methods. Continuing developments to implement these procedures into an enhanced version of SPAR are also discussed.
Repeated or closely packed modal frequencies are common physical occurrences for vibrating structures which are complex or possess multi-planes of symmetry. The computation of the sensitivity to structural modifications for these frequencies and mode shapes is made difficult by the fact that the mode shapes are not unique, since any linear combination of eigenvectors corresponding to a repeated eigenvalue is also an eigenvector. The work of Chen and Pan is extended, who used modal expansion techniques for accommodating the sensitivity analysis of structures with repeated eigenvalues. Starting with a discussion of the physical significance of sensitivity analysis for repeated frequency modes, a derivation is presented of the governing equations for the derivatives of a repeated eigenvalue. This is followed with a small example to illustrate the results. An efficient computation procedure, based upon an expansion of Nelson's ideas for large banded systems, is then proposed for systems with repeated or closely spaced eigenvalues.
The direct, singular, boundary element analysis formulation is shown to provide a basis for a computationally efficient and accurate shape design sensitivity analysis approach for the structural response of three-dimensional solid objects. The theoretical formulation for surface displacement and traction component sensitivities, and all components of the stress tensor is presented along with a formulation for the recovery of displacement and stress components in the interior of the object under consideration. Discussion of computational issues related to the overall efficiency of these formulations is given, along with numerical results to demonstrate the accuracy and efficiency of this approach.
Maximum likelihood estimation of parameters in linear structural relationships under normality assumptions requires knowledge of one or more of the model parameters if no replication is available. The most common assumption added to the model definition is that the ratio of the error variances of the response and predictor variates is known. The use of asymptotic formulae for variances and mean squared errors as a function of sample size and the assumed value for the error variance ratio is investigated.