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.

/pdf/recent-developments-in-structural-sensitivity-analysis-23fy9nqyl5.pdf

Recent developments in structural sensitivity analysis

Design sensitivity analysis of non‐linear structural systems part I: Theory

In this paper, a mixed approach for probabilistic structural durability design of mechanical systems is proposed. In this approach, a deterministic design optimization that considers structural crack initiation and crack propagation lives at critical points of the structural component as design constraints is performed first. After an optimal design is obtained, a reliability analysis is performed to ascertain if the deterministic optimal design is reliable. If the probability of the failure of the deterministic optimal design is found to be acceptable, a reliability-based design approach that employs a set of interactive design steps, such as trade-off analysis and what-if study, is used to obtain a near-optimal design that is reliable with an affordable computational cost. A 3-D tracked vehicle roadarm is employed to demonstrate the feasibility of the proposed approach.

A mixed design approach for probabilistic structural durability

A unified method for continuum shape design sensitivity analysis and optimal design of mechanical components is developed. A domain method of shape design sensitivity analysis that uses the material derivative concept of continuum mechanics is employed. For numerical implementation of shape optimal design, parameterization of the boundary shape of mechanical components is defined and illustrated using a Bezier surface. In shape design problems, nodal points of the finite element model move as the shape changes. A method of automatic regridding to account for shape change has been developed using a design velocity field in the physical domain that obeys the governing equilibrium equations of the elastic solid. For numerical implementation of the continuum shape design sensitivity analysis and automatic regridding, an established finite element analysis code is used. To demonstrate the feasibility of the method developed, shape design optimization of a main engine bearing cap is carried out as an example.

3‐D shape optimal design and automatic finite element regridding

Anefe cientreliability analysis method fordurability of structural components subjected to external and inertial loads with time-dependent variable amplitudes is presented. This method is able to support reliability analysis of crack-initiation and crack-propagation lives of practical applications, considering uncertainties such as material properties, manufacturing tolerances, and initial crack size. Three techniques are employed to support the probabilistic durability prediction: 1 ) strain-based approach for multiaxial crack-initiation-life prediction and linear elastic fracture mechanics approach for crack-propagation-life prediction, 2 ) statistics-based approach for reliability analysis, and 3 ) sensitivity analysis and optimization methods for searching the most probable point (MPP) in the random variable space to compute the fatigue failure probability using the e rst-order reliability analysis method. A two-point approximation method is employed to speed up the MPP search. A tracked-vehicle roadarm is presented to demonstrate feasibility of the proposed method.

Probabilistic Structural Durability Prediction

A numerical method is presented to implement structural design sensitivity analysis theory, using the versatility and convenience of existing finite element structural analysis programs. Design variables such as thickness and cross-sectional areas of components of individual members and built-up structures are considered. Structural performance functionals considered include displacement and stress. The method is also applicable for eigenvalue problem design sensitivity analysis. It is shown that calculations can be carried out outside existing finite element codes, using postprocessing data only. Thus, design sensitivity analysis software does not have to be embedded in an existing finite element code. Feasability of the method is shown through analysis of several problems, including a built-up structure. Accurate design sensitivity results are obtained without the uncertainty of numerical accuracy associated with selection of finite difference perturbations.

Implementation of Design Sensitivity Analysis with Existing Finite Element Codes

A numerical method is presented to implement structural design sensitivity analysis using the versatility and convenience of existing finite element structural analysis program and the theoretical foundation in structural design sensitivity analysis. Conventional design variables, such as thickness and cross-sectional areas, are considered. Structural performance functionals considered include compliance, displacement, and stress. It is shown that calculations can be carried out outside existing finite element codes, using postprocessing data only. That is, design sensitivity analysis software does not have to be imbedded in an existing finite element code. The finite element structural analysis program used in the implementation presented is IFAD. Feasibility of the method is shown through analysis of several problems, including built-up structures. Accurate design sensitivity results are obtained without the uncertainty of numerical accuracy associated with selection of a finite difference perturbation.

https://ntrs.nasa.gov/api/citations/19870017787/downloads/19870017787.pdf

Design sensitivity analysis with Applicon IFAD using the adjoint variable method

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Implementation of Design Sensitivity Analysis with Existing Finite Element Codes

Design sensitivity analysis with Applicon IFAD using the adjoint variable method