Search results

This paper aims to present a new method, named as augmented polynomial dimensional decomposition (PDD) method, for robust design optimization (RDO) and reliability-based design optimization (RBDO) subject to mixed design variables comprising both distributional and structural design variables.

The method involves a new augmented PDD of a high-dimensional stochastic response for statistical moments and reliability analyses; an integration of the augmented PDD, score functions, and finite-difference approximation for calculating the sensitivities of the first two moments and the failure probability with respect to distributional and structural design variables; and standard gradient-based optimization algorithms.

New closed-form formulae are presented for the design sensitivities of moments that are simultaneously determined along with the moments. A finite-difference approximation integrated with the embedded Monte Carlo simulation of the augmented PDD is put forward for design sensitivities of the failure probability.

In conjunction with the multi-point, single-step design process, the new method provides an efficient means to solve a general stochastic design problem entailing mixed design variables with a large design space. Numerical results, including a three-hole bracket design, indicate that the proposed methods provide accurate and computationally efficient sensitivity estimates and optimal solutions for RDO and RBDO problems.

In the reliability assessment of composite laminate structures with multiple components, the uncertainty space defined around design solutions easily becomes over-dimensioned, and not all of the random variables are relevant. The purpose of this study is to implement the importance analysis theory of Sobol’ to reduce the dimension of the uncertainty space, improving the efficiency toward global convergence of evolutionary-based reliability assessment.

Sobol’ indices are formulated analytically for implicit structural response functions, following the theory of propagation of moments and without violating the fundamental principles presented by Sobol’. An evolutionary algorithm capable of global convergence in reliability assessment is instrumented with the Sobol’ indices. A threshold parameter is introduced to identify the important variables. A set of optimal designs of a multi-laminate composite structure is evaluated.

Importance analysis shows that uncertainty is concentrated in the laminate where the critical stress state is found. Still, it may also be reasonable in other points of the structure. An accurate and controlled reduction of the uncertainty space significantly improves the convergence rate, while maintaining the quality of the reliability assessment.

The theoretical developments assume independent random variables.

Applying Sobol’ indices as an analytical dimension reduction technique is a novelty. The proposed formulation only requires one adjoint system of equilibrium equations to be solved once. Although a local estimate of a global measure, this analytical formulation still holds because, in structural design, uncertainty is concentrated around the mean-values.

The purpose of this paper is to develop a meshless numerical method for three‐dimensional isotropic thermoelastic problems with arbitrary body forces.

This paper combines the method of fundamental solutions (MFS) and the dual reciprocity method (DRM) as a meshless numerical method (MFS‐DRM) to solve three‐dimensional isotropic thermoelastic problems with arbitrary body forces. In the DRM, the arbitrarily distributed temperature and body force are approximated by polyharmonic splines with augmented polynomial basis, whose particular solutions and the corresponding tractions are reviewed and given explicitly. The MFS is then applied to solve the complementary solution. Numerical experiments of Dirchlet, Robin, and peanut‐shaped‐domain problems are carried out to validate the method.

In literature, it is commented that the Gaussian elimination can be used reliably to solve the MFS equations for non‐noisy boundary conditions. For noisy boundary conditions, the truncated singular value decomposition (TSVD) is more accurate than the Gaussian elimination. In this paper, it was found that the particular solutions obtained by the DRM act like noises and the use of TSVD improves the accuracy.

It is the first time that the MFS‐DRM is derived to solve three‐dimensional isotropic thermoelastic problems with arbitrary body forces.

This paper describes the solution of a steady‐state natural convection problem in porous media by the radial basis function collocation method (RBFCM). This mesh‐free (polygon‐free) numerical method is for a coupled set of mass, momentum, and energy equations in two dimensions structured by the Hardy's multiquadrics with different shape parameter and different order of polynomial augmentation. The solution is formulated in primitive variables and involves iterative treatment of coupled pressure, velocity, pressure correction, velocity correction, and energy equations. Numerical examples include convergence studies with different collocation point density and arrangements for a two‐dimensional differentially heated rectangular cavity problem at filtration Rayleigh numbers Ra*=25, 50 and 100, and aspect ratios A=1/2, 1, and 2. The solution is assessed by comparison with reference results of the fine‐mesh finite volume method in terms of mid‐plane velocity components, mid‐plane and insulated surface temperatures, streamfunction minimum, and Nusselt number.

We compare methods to measure comovement in business cycle data using multi-level dynamic factor models. To do so, we employ a Monte Carlo procedure to evaluate model performance for different specifications of factor models across three different estimation procedures. We consider three general factor model specifications used in applied work. The first is a single-factor model, the second a two-level factor model, and the third a three-level factor model. Our estimation procedures are the Bayesian approach of Otrok and Whiteman (1998), the Bayesian state-space approach of Kim and Nelson (1998) and a frequentist principal components approach. The latter serves as a benchmark to measure any potential gains from the more computationally intensive Bayesian procedures. We then apply the three methods to a novel new dataset on house prices in advanced and emerging markets from Cesa-Bianchi, Cespedes, and Rebucci (2015) and interpret the empirical results in light of the Monte Carlo results.

A consistent formulation for unilateral contact problems including frictional work hardening or softening is proposed. The approach is based on an augmented Lagrangian approach coupled to an implicit quasi‐static Finite Element Method. Analogous to classical work hardening theory in elasto‐plasticity, the frictional work is chosen as the internal variable for formulating the evolution of the friction convex. In order to facilitate the implementation of a wide range of phenomenological models, the friction coefficient is defined in a parametrised form in terms of Bernstein polynomials. Numerical simulation of a 3D deep‐drawing operation demonstrates the performance of the methods for predicting frictional contact phenomena in the case of large sliding paths including high curvatures.

Contemporary stochastic optimal control by synergy of the probability density evolution method (PDEM) and conventional optimal controller exhibits less capability to guarantee economical energy consumption versus control efficacy when non-stationary stochastic excitations drive hysteretic structures. In this regard, a novel multiscale stochastic optimal controller is invented based on the wavelet transform and the PDEM.

For a representative point, a conventional control law is decomposed into sub-control laws by deploying the multiresolution analysis. Then, the sub-control laws are classified into two generic control laws using resonant and non-resonant bands. Both frequency bands are established by employing actual natural frequency(ies) of structure, making computed efforts depend on actual structural properties and time-frequency effect of non-stationary stochastic excitations. Gain matrices in both bands are then acquired by a probabilistic criterion pertaining to system second-order statistics assessment. A multi-degree-of-freedom hysteretic structure driven by non-stationary and non-Gaussian stochastic ground accelerations is numerically studied, in which three distortion scenarios describing uncertainties in structural properties are considered.

Time-frequency-dependent gain matrices sophisticatedly address non-stationary stochastic excitations, providing efficient ways to independently suppress vibrations between resonant and non-resonant bands. Wavelet level, natural frequency(ies), and ratio of control forces in both bands influence the scheme’s outcomes. Presented approach outperforms existing approach in ensuring trade-off under uncertainty and randomness in system and excitations.

Presented control law generates control efforts relying upon resonant and non-resonant bands, and deploys actual structural properties. Cost-function weights and probabilistic criterion are promisingly developed, achieving cost-effectiveness of energy demand versus controlled structural performance.

This study aims to treat a novel system of Volterra integro-differential equations with multiple delays and variable bounds, constituting a generic numerical method based on the matrix equation and a combinatoric-parametric Charlier polynomials. The proposed method utilizes these polynomials for the matrix relations at the collocation points.

Thanks to the combinatorial eligibility of the method, the functional terms can be transformed into the generic matrix relations with low dimensions, and their resulting matrix equation. The obtained solutions are tested with regard to the parametric behaviour of the polynomials with $\alpha$, taking into account the condition number of an outcome matrix of the method. Residual error estimation improves those solutions without using any external method. A calculation of the residual error bound is also fulfilled.

All computations are carried out by a special programming module. The accuracy and productivity of the method are scrutinized via numerical and graphical results. Based on the discussions, one can point out that the method is very proper to solve a system in question.

This paper introduces a generic computational numerical method containing the matrix expansions of the combinatoric Charlier polynomials, in order to treat the system of Volterra integro-differential equations with multiple delays and variable bounds. Thus, the method enables to evaluate stiff differential and integral parts of the system in question. That is, these parts generates two novel components in terms of unknown terms with both differentiated and delay arguments. A rigorous error analysis is deployed via the residual function. Four benchmark problems are solved and interpreted. Their graphical and numerical results validate accuracy and efficiency of the proposed method. In fact, a generic method is, thereby, provided into the literature.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.