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This paper presents a new framework to predict a structure’s effective properties and sensitivities to multiple simultaneous uncertain endogenous parameters. The methodology is based on the use of fuzzy sets and this paper extends the fuzzy set theory to a dynamic finite element analysis of engineering systems containing uncertainty on material properties. A general algorithm, which can resolve the uncertain eigenvalue problem by using a Neumann expansion, is studied. This algorithm is applied to the study of the modal behavior of structures presenting uncertain material properties. Finally, the entropy and the specificity of fuzzy responses lead to the identification of a plate structure’s most sensitive eigenvalue to uncertain sources.

The purpose of this paper is to expand the previously published fuzzy logic controller for contact method to normal frictionless contact for solving mechanical frictional contact problems. The secondary aim is to integrate a reduction model for each component in contact to decrease the size of the global finite element contact problem.

The proposed strategy relies on the design of two fuzzy logic controllers currently used in the automation domain. These controllers are considered to link normal and tangential gaps (for sticking conditions) with normal and tangential contact loads. A direct consequence of integrating a control-based approach into the numerical solving approach is the decomposition of the non-linear problem into a set of linear problems.

With this new strategy, no tangent or coupling matrix is defined for the contact problem that allows to consider a projection matrix to reduce the size of each component in contact and subsequently to decrease the associated computational time. As in condensation techniques, this matrix is composed of both modal bases of each component in contact and static modes that capture behaviors at the contact interface. Moreover, the proposed numerical application highlights the efficiency of the proposal in terms of computation time and precision of contact data.

The developments are currently implemented in Matlab only for 2D static numerical applications. Therefore, as obtained results are very promising in terms of precision and computational time, the objective is to complete the proposed method in future research to manage frictional contact for 3D finite element models in a dynamic context.

In conclusion, this paper highlights the interest of studying mechanical frictional contact problems by considering fuzzy logic control approaches.

The purpose of this paper is to present a new way to solve numerically a mechanical frictionless contact problem within a context of multiple sampling, frequently used to design robust structures.

This paper proposes to integrate a control-based approach, currently used in automation domain, for the solving of non-linear mechanical problem. More precisely, a fuzzy logic controller is designed to create a link between the normal gaps identified between the bodies and the normal contact pressures applied at the interface.

With this new strategy, the initial non-linear problem can be decomposed into a set of reduced linear problems solved using the finite element method. A projection built from the modal bases of each component in contact is considered to reduce computational time. Moreover, the proposed numerical applications highlight an interesting compromise between computation time and precision of contact data.

Currently, the proposed Fuzzy Logic Controller for Contact method has been developed for a frictionless contact problem in the case of 2D numerical applications. Therefore, as obtained results are very interesting, it will be possible to expand on these works in a future works for more complex problems including friction, 3D model and transient dynamic responses by adding other controllers.

In conclusion, this paper highlights the interest of studying a contact problem by considering automation approaches and defines the basis of future multidisciplinary works.

This paper presents an efficient methodology to calculate fuzzy eigenvalues and eigenvectors of finite element structures defined by imprecise parameters. The material and geometric parameters are then described by fuzzy numbers. The proposed methodology, based on α‐cut discretization of fuzzy numbers and Taylor's expansion, determines the extreme eigensolutions for each α‐cut. The study of a finite element model and the comparison of results with a combinatorial approach, based on Zadeh's extension principle, show the efficiency of this methodology.

Considers the problem of structures’ sensitivities to prescribed displacements uncertainties through the use of fuzzy numbers. Important properties of fuzzy subsets have been studied and used to model uncertainties, and to solve the fuzzy linear system resulting from taking into account the uncertainties on prescribed displacements. Develops a computer program to allow comparisons between several structural designs checking common specifications. Demonstrates the effectiveness of the present method for a cantilever structure modelled in the case of a static finite element analysis.

This paper aims to propose a gradient-based shape optimization framework in which traditional time-consuming conversions between computer-aided design and computer-aided engineering and the mesh update procedure are avoided/eliminated. The scheme is general so that it can be used in all cases as a black box, no matter what the objective and/or design variables are, whilst the efficiency and accuracy are guaranteed.

The authors integrated CAD and CAE by using isogeometric analysis (IGA), enabling the present methodology to be robust and accurate. To overcome the difficulty in evaluating the sensitivities of objective and/or constraint functions by analytic method in some cases, the authors adopt the finite difference method to calculate these sensitivities, thereby providing a universal approach. Moreover, to further eliminate the inefficiency caused by the finite difference method, the authors advance the exact reanalysis method, the indirect factorization updating (IFU), to exactly and efficiently calculate functions and their sensitivities, which guarantees its generality and efficiency at the same time.

The proposed isogeometric gradient-based shape optimization using our IFU approach is reliable and accurate, as well as general and efficient.

The authors proposed a gradient-based shape optimization framework in which they first integrate IGA and the proposed exact reanalysis method for applicability to structural response and sensitivity analysis.

Many analysis and design problems in engineering and science involve uncertainty to varying degrees. This paper is concerned with the structural vibration problem involving uncertain material or geometric parameters, specified as fuzzy parameters. The requirement is to propagate the parameter uncertainty to the eigenvalues of the structure, specified as fuzzy eigenvalues. However, the usual approach is to transform the fuzzy problem into several interval eigenvalue problems by using the α-cuts method. Solving the interval problem as a generalized interval eigenvalue problem in interval mathematics will produce conservative bounds on the eigenvalues. The purpose of this paper is to investigate strategies to efficiently solve the fuzzy eigenvalue problem.

Based on the fundamental perturbation principle and vertex theory, an efficient perturbation method is proposed, that gives the exact extrema of the first-order deviation of the structural eigenvalue. The fuzzy eigenvalue approach has also been improved by reusing the interval analysis results from previous α-cuts.

The proposed method was demonstrated on a simple cantilever beam with a pinned support, and produced very accurate fuzzy eigenvalues. The approach was also demonstrated on the model of a highway bridge with a large number of degrees of freedom.

This proposed Vertex-Perturbation method is more efficient than the standard perturbation method, and more general than interval arithmetic methods requiring the non-negative decomposition of the mass and stiffness matrices. The new increment method produces highly accurate solutions, even when the membership function for the fuzzy eigenvalues is complex.

The purpose of this paper is to propose a unified optimization design method and apply it to handle the brake squeal instability involving various uncertainties in a unified framework.

Fuzzy random variables are taken as equivalent variables of conventional uncertain variables, and a unified response analysis method is first derived based on level-cut technique, Taylor expansion and central difference scheme. Next, a unified reliability analysis method is developed by integrating the unified response analysis and fuzzy possibility theory. Finally, based on the unified reliability analysis method, a unified reliability-based optimization model is established, which is capable of optimizing uncertain responses in a unified way for different uncertainty cases.

The proposed method is extended to perform squeal instability analysis and optimization involving various uncertainties. Numerical examples under eight uncertainty cases are provided and the results demonstrate the effectiveness of the proposed method.

Most of the existing methods of uncertainty analysis and optimization are merely effective in tackling one uncertainty case. The proposed method is able to handle the uncertain problems involving various types of uncertainties in a unified way.

The purpose of this paper is to develop an analytical approach to evaluate the influence of material uncertainties on cross‐sectional stiffness properties of thin walled composite beams.

Fuzzy arithmetic operators are used to modify the thin‐walled beam formulation, which was based on a mixed force and displacement method, and to obtain the uncertainty properties of the beam. The resulting model includes material uncertainties along with the effects of elastic couplings, shell wall thickness, torsion warping and constrained warping. The membership functions of material properties are introduced to model the uncertainties of material properties of composites and are determined based on the stochastic behaviors obtained from experimental studies.

It is observed from the numerical studies that the fuzzy membership function approach results in reliable representation of uncertainty quantification of thin walled composite beams. The propagation of uncertainties is also demonstrated in the estimation of structural responses of composite beams.

This work demonstrates the use of fuzzy approach to incorporate uncertainties in the responses analytically, in turn improving computational efficiency drastically as compared to the Monte‐Carlo method.

This study considers a Lagrange direct way of modal assurance criterion (MAC) values of an undamped system. The mentioned method for the sensitivity analysis of the MAC of a sliding machine working table is more close to the exact solution and time efficient. The paper aims to discuss these issues.

Using the Lagrange multipliers to compute the first and second-order sensitivity analysis of MAC values.

Because of the Lagrange multiplier without considering the number of design parameters, one only needs to perform the calculation once. Compared with the indirect way, the direct way is more effective when the number of design parameters is greater than one. This calculation procedure is simple and accurate, which can be popularized and used.

Engineering structure often requires only some structure design, and most of the sub-structure design variables are not related to each other. In this case, this way is better and more efficient. The direct way can be applied to the dynamic optimization design of large structures, the frequency and the mode sensitivity analysis in the process of model modification.