Microstructural topology optimization for minimizing the sound pressure level of structural–acoustic coupled systems with multi-scale random parameters

The main aim of this article is to present a robust microstructural topology optimization methodology for structural–acoustic coupled systems with multi-scale random parameters. During the microstructural topology optimization, both the uncertainty at the macro-scale, which comes from the physical parameters of the acoustic medium or the external load, and the uncertainty existing in the constituent material properties of the microstructure at the micro-scale are considered as random parameters. A homogenization-based probabilistic finite element method (HPFEM) is first developed for quantifying the structural–acoustic system with multi-scale random parameters. The use of the HPFEM transforms the problem of microstructural topology optimization with multi-scale random parameters to an augmented deterministic microstructural topology optimization problem. This provides a computationally cheap alternative to Monte Carlo-based optimization algorithms. A numerical example of a hexahedral box is given to demonstrate the efficiency of the proposed method.     

Synthesis of porous–acoustic absorbing systems by an evolutionary optimization method

Topology optimization is frequently used to design structures and acoustic systems in a large range of engineering applications. In this work, a method is proposed for maximizing the absorbing performance of acoustic panels by using a coupled finite element model and evolutionary strategies. The goal is to find the best distribution of porous material for sound absorbing panels. The absorbing performance of the porous material samples in a Kundt tube is simulated using a coupled porous–acoustic finite element model. The equivalent fluid model is used to represent the foam material. The porous material model is coupled to a wave guide using a modal superposition technique. A sensitivity number indicating the optimum locations for porous material to be removed is derived and used in a numerical hard kill scheme. The sensitivity number is used to form an evolutionary porous material optimization algorithm which is verified through examples.     

A level set–based method for stress-constrained multimaterial topology optimization of minimizing a global measure of stress

In multimaterial topology optimization of minimizing a global measure of stress, the maximum stresses in different materials may not satisfy the strength design requirements simultaneously if stress constraints for different materials are not considered. In this paper, a level set–based method is presented to handle the stress-constrained multimaterial topology optimization of minimizing a global stress measure. Specifically, a multimaterial level set model is adopted to describe the structural topology, and a stress interpolation scheme is introduced for stress evaluation. Then, a stress penalty-based topology optimization model is presented. Meanwhile, an adaptive adjusting scheme of the stress penalty factor is employed to improve the control of the local stress level. To solve the stress-constrained multimaterial topology optimization problem minimizing the global measure of stress, the parametric level set method is employed, and the sensitivity analysis is carried out. Numerical examples are provided to demonstrate the effectiveness of the presented method. Results indicate that multimaterial structures with optimized global stress can be gained, and stress constraints for different materials can be satisfied simultaneously.     

Development of a multidisciplinary–multiresponse robust design optimization model

Robust design is an efficient process improvement methodology that combines experimentation with optimization to create systems that are tolerant to uncontrollable variation. Most traditional robust design models, however, consider only a single quality characteristic, yet customers judge products simultaneously on a variety of scales. Additionally, it is often the case that these quality characteristics are not of the same type. To addresses these issues, a new robust design optimization model is proposed to solve design problems involving multiple responses of several different types. In this new approach, noise factors are incorporated into the robust design model using a combined array design, and the results of the experiment are optimized using a new approach that is formulated as a nonlinear goal programming problem. The results obtained from the proposed methodology are compared with those of other robust design methods in order to examine the trade-offs between meeting the objectives associated with different optimization approaches.     

Asymptotical construction of a fully coupled,Reissner–Mindlin model for piezoelectric and piezomagnetic laminates

The variational asymptotic method is used to construct a fully coupled Reissner–Mindlin model for piezoelectric and piezomagnetic laminates with some surfaces parallel to the reference surface coated with electrodes and magnetism. Taking advantage of the smallness of the plate thickness, we asymptotically split the original 3D electromagneto-mechanical problem into a 1D through-the-thickness analysis and a 2D plate analysis, and both are fully-coupled multiphysics analyses. The through-the-thickness analysis serves as a link between the original 3D analysis and the plate analysis by providing a constitutive model for the plate analysis and recovering the 3D field variables in terms of global responses calculated by the plate analysis. The present theory is implemented into the computer program VAPAS (Variational Asymptotic Plate and Shell Analysis). A numerical example of three-layer sandwich plate has been used to validate the present model.     

Performance optimization of a miniature Joule–Thomson cryocooler using numerical model

The performance of a miniature Joule–Thomson cryocooler depends on the effectiveness of the heat exchanger. The heat exchanger used in such cryocooler is Hampson-type recuperative heat exchanger. The design of the efficient heat exchanger is crucial for the optimum performance of the cryocooler.In the present work, the heat exchanger is numerically simulated for the steady state conditions and the results are validated against the experimental data available from the literature. The area correction factor is identified for the calculation of effective heat transfer area which takes into account the effect of helical geometry. In order to get an optimum performance of the cryocoolers, operating parameters like mass flow rate, pressure and design parameters like heat exchanger length, helical diameter of coil, fin dimensions, fin density have to be identified. The present work systematically addresses this aspect of design for miniature J–T cryocooler.     

A coupled symmetric BE–FE method for acoustic fluid–structure interaction

A coupled symmetric BE–FE method for the calculation of linear acoustic fluid–structure interaction in time and frequency domain is presented. In the coupling formulation a newly developed hybrid boundary element method (HBEM) will be used to describe the behaviour of the compressible fluid. The HBEM is based on Hamilton's principle formulated with the velocity potential. The state variables are separated into boundary variables which are approximated by piecewise polynomial functions and domain variables which are approximated by a superposition of static fundamental solutions. The domain integrals are eliminated, respectively, replaced by boundary integrals and a boundary element formulation with a symmetric mass and stiffness matrix is obtained as result. The structure is discretized by FEM. The coupling conditions fulfil C¹-continuity on the interface. The coupled formulation can also be used for eigenfrequency analyses by transforming it from time domain into frequency domain.     

Multidimensional parallelepiped model—a new type of non-probabilistic convex model for structural uncertainty analysis

Non-probabilistic convex models need to be provided only the changing boundary of parameters rather than their exact probability distributions; thus, such models can be applied to uncertainty analysis of complex structures when experimental information is lacking. The interval and the ellipsoidal models are the two most commonly used modeling methods in the field of non-probabilistic convex modeling. However, the former can only deal with independent variables, while the latter can only deal with dependent variables. This paper presents a more general non-probabilistic convex model, the multidimensional parallelepiped model. This model can include the independent and dependent uncertain variables in a unified framework and can effectively deal with complex ‘multi-source uncertainty’ problems in which dependent variables and independent variables coexist. For any two parameters, the concepts of the correlation angle and the correlation coefficient are defined. Through the marginal intervals of all the parameters and also their correlation coefficients, a multidimensional parallelepiped can easily be built as the uncertainty domain for parameters. Through the introduction of affine coordinates, the parallelepiped model in the original parameter space is converted to an interval model in the affine space, thus greatly facilitating subsequent structural uncertainty analysis. The parallelepiped model is applied to structural uncertainty propagation analysis, and the response interval of the structure is obtained in the case of uncertain initial parameters. Finally, the method described in this paper was applied to several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Application of inserts for suppression of coupled dynamic–acoustic effects during confined granular flow in silos

The paper discusses methods to prevent coupled dynamic–acoustic effects during silo flow by means of inserts. Laboratory tests were carried out with a perspex and steel model silo with different inserts along the wall. As bulk solids, sand, polymer granulate and PET flakes were used. An effective method for a reduction of dynamic–acoustic phenomena during silo flow was elaborated. It was verified in large metal silos.     

A parameter optimization heuristic for a temperature estimation model

We present a heuristic technique for solving a parameter estimation problem that arises in modeling the thermal behavior of electronic chip packages. Compact Thermal Models (CTMs) are network models of steady state thermal behavior, which show promise in augmenting the use of more detailed and computationally expensive models. The CTM parameter optimization problem that we examine is a nonconvex optimization problem in which we seek a set of CTM parameters that best predicts, under general conditions, the thermal response of a particular chip package geometry that has been tested under a small number of conditions. We begin by developing a nonlinear programming formulation for this parameter optimization problem, and then develop an algorithm that uses special characteristics of the optimization problem to quickly generate heuristic solutions. Our algorithm descends along a series of solutions to one-dimensional nonconvex optimization problems, obtaining a locally optimal set of model parameters at modest computational cost. Finally, we provide some experimental results and recommendations for extending this research. The authors are indebted to four anonymous referees for their help in improving the contribution and presentation of this paper.     

Unified structural–procedural approach for designing integrated manufacturing systems

A manufacturing system consists of a structure and distributed working procedures that include operating parameters. A new approach named unified structural–procedural approach (USPA) for designing the integrated structure and the distributed but integrated working procedures of a manufacturing system is included in this paper. The designed structure and working procedures bring about the efficiency desired by the target market on the ordered products even when the desired efficiency is turbulent. Here, the USPA approach is applied to redesign a real apparel factory. The USPA includes identification of the target market requirements, conception of the target manufacturing system, design of the system structure and working procedures. Conception of the target manufacturing system is done using pseudo-neural networks that exploit the improvements introduced by the higher performing firms throughout the industry. Design of the system structure is done using simulation models that bring forth building structural improvements whose implementation investments equate the saved inefficiency costs because the system structure is improved. The distributed working procedures are specified using flowcharts that include integrated values of the procedural parameters. The nature of these parameters are identified from available non-integrated operations management models and their integrated values obtained by using simulation models that evaluate their joint effect on product efficiency.     

Elastic crack propagation model for crystalline solids using a self-consistent coupled atomistic–continuum framework

Deformation and failure processes of crystalline materials are governed by complex phenomena at multiple scales. It is necessary to couple these scales for physics-based modeling of these phenomena, while overcoming limitations of modeling at individual scales. To address this issue, this paper develops self-consistent elastic constitutive and crack propagation relations of crystalline materials containing atomic scale cracks, from observations made in a concurrent multi-scale simulation system coupling atomistic and continuum domain models. The concurrent multi-scale model incorporates a finite temperature atomistic region containing the crack, a continuum region represented by a self-consistent crystal elasticity constitutive model, and a handshaking interphase region. Atomistic modeling is done by the molecular dynamics code LAMMPS, while continuum modeling is conducted by the finite element method. For single crystal nickel a nonlinear and nonlocal crystal elasticity constitutive relation is derived, consistent with the atomic potential function. An efficient, staggered solution scheme with parallel implementation is designed for the coupled problem. The atomistic–continuum coupling is achieved by enforcing geometric compatibility and force equilibrium in the interphase region. Quantitative analyses of the crack propagation process focuses on size dependence, strain energy release rate, crack propagation rate and degradation of the local stiffness. The self-consistent constitutive and crack propagation relations, derived from the concurrent model simulation results are validated by comparing results from the concurrent and full FE models. Excellent accuracy and enhanced efficiency are observed in comparison with pure MD and concurrent model results.     

Dynamical theoretical model and variational principles for coupled temperature–diffusion–mechanics

In this paper, firstly, the acceleration of the temperature and concentration are assumed to need the extra increment of the heat and energy. The inertial entropy and the inertial chemical potential were proposed by Kuang (Acta Mech 203:1–11, 2009, Acta Mech 214:275–289, 2010). Secondly, the expressions of dissipative energy produced by the variation of the temperature and concentration are derived by using the second law of thermodynamics. Finally, several variational principles for coupled temperature–diffusion–mechanics are established, and their corresponding governing equations and boundary conditions are naturally presented. Meanwhile, some numerical simulations are carried out to describe the coupled reciprocity, which shows concentration diffusion with a finite velocity.     

Cost optimization for series–parallel execution of a collection of intersecting operation sets

A collection of intersecting sets of operations is considered. These sets of operations are performed successively. The operations of each set are activated simultaneously. Operation durations can be modified. The cost of each operation decreases with the increase in operation duration. In contrast, the additional expenses for each set of operations are proportional to its time. The problem of selecting the durations of all operations that minimize the total cost under constraint on completion time for the whole collection of operation sets is studied. The mathematical model and method to solve this problem are presented. The proposed method is based on a combination of Lagrangian relaxation and dynamic programming. The results of numerical experiments that illustrate the performance of the proposed method are presented. This approach was used for optimization multi-spindle machines and machining lines, but the problem is common in engineering optimization and thus the techniques developed could be useful for other applications.     

Development of a reduced-order model for large-scale Eulerian–Lagrangian simulations

Multiphase flows with solid particles are commonly encountered in various industries. The CFD–DEM method is extensively used to simulate their dynamical behavior. However, the application of the CFD–DEM method to simulate industrial-scale powder processes unavoidably leads to huge computational costs. With the aim of overcoming this issue, we propose a nonintrusive reduced-order model for Eulerian–Lagrangian simulations (ROM-EL) to efficiently reproduce gas–solid flow in fluidized beds. In the model, a Lanczos based proper orthogonal decomposition (LPOD) is newly employed to efficiently generate a set of POD bases. After the numerical snapshots are projected onto the reduced space spanned by the POD bases, a series of multidimensional functions of POD coefficients are constructed using a surrogate interpolation method. To demonstrate the effectiveness of this model, validation studies are performed based on the simulations of a fluidized bed. The macroscopic properties, such as the particle distribution, bed height, pressure drop, and distribution of bubble size, are shown to agree well in the CFD–DEM model and ROM-EL. Further, our proposed ROM-EL reduces the computational cost by several orders of magnitude compared with the CFD–DEM simulation. Accordingly, the ROM-EL could significantly contribute to the progress of modeling and simulation for industrial granular flows.     

A nonprobabilistic reliability–based topology optimization method of compliant mechanisms with interval uncertainties

On account of the inevitable multisource uncertainty factors in compliant mechanisms, which seriously affect the accuracy of output motion, a nonprobabilistic reliability–based topology optimization (NRBTO) framework for compliant mechanisms with interval uncertainties is introduced. Combined with the solid isotropic material with penalization (SIMP) model and the set-theoretical interval method, the uncertainty quantification analysis is conducted to obtain mathematical approximations and boundary laws of considered mean compliance. By normalization treatment of the limit-state function, a new quantified measure of the nonprobabilistic reliability is then defined. The compliance-based NRBTO design method ensures the output motion realizing its target value accurately considering the uncertainty factors. The sensitivities of the nonprobabilistic reliability index with respect to design variables are calculated by the adjoint vector method. Two engineering examples are eventually presented to illustrate the applicability and the validity of the present problem statement as well as the proposed numerical techniques.     

Truss topology optimization with static and dynamic constraints using modified subpopulation teaching–learning-based optimization

In this study, an improved version of the teaching–learning-based optimization (TLBO) algorithm is proposed for truss topology optimization (TTO), with static and dynamic constraints on planar and space trusses. The basic TLBO algorithm is improved to enhance its exploration and exploitation abilities by considering various factors such as the number of teachers, adaptive teaching, tutorial learning and self-motivated learning. The TTO problems are considered with multiple load conditions and subjected to constraints for natural frequencies, element stresses, nodal displacements, Euler buckling criteria and kinematic stability conditions. TTO is achieved with the removal of superfluous elements and nodes from the ground structure, and results in a mass saving. In this method, difficulties arise owing to singular solution and unnecessary analysis; therefore, the finite element model is reformed to resolve these issues. A single-stage optimization approach is used, in which size and topology optimization are considered simultaneously. The results obtained are compared with the best solutions obtained by the algorithm. The results reveal that the modified subpopulation teaching–learning-based optimization (MS-TLBO) algorithm is more effective than other state-of-the-art algorithms.     

Developing a fuzzy proportional–derivative controller optimization engine for engineering design optimization problems

In real world engineering design problems, decisions for design modifications are often based on engineering heuristics and knowledge. However, when solving an engineering design optimization problem using a numerical optimization algorithm, the engineering problem is basically viewed as purely mathematical. Design modifications in the iterative optimization process rely on numerical information. Engineering heuristics and knowledge are not utilized at all. In this article, the optimization process is analogous to a closed-loop control system, and a fuzzy proportional–derivative (PD) controller optimization engine is developed for engineering design optimization problems with monotonicity and implicit constraints. Monotonicity between design variables and the objective and constraint functions prevails in engineering design optimization problems. In this research, monotonicity of the design variables and activities of the constraints determined by the theory of monotonicity analysis are modelled in the fuzzy PD controller optimization engine using generic fuzzy rules. The designer only needs to define the initial values and move limits of the design variables to determine the parameters in the fuzzy PD controller optimization engine. In the optimization process using the fuzzy PD controller optimization engine, the function value of each constraint is evaluated once in each iteration. No sensitivity information is required. The fuzzy PD controller optimization engine appears to be robust in the various design examples tested.     

Modified Reynolds equation for coupled stress fluids – a porous media model

Summary. In this paper, the rheological effects of coupled stress fluids on thin film lubrication modeling are developed. Thin porous layers attached to the impermeable substrate are utilized to model the microstructure of bearing surfaces. In the fluid film region, the constitutive equations for coupled stress fluids proposed by Stokes [1] as well as the continuity and momentum equations are applied to model the flow. In the porous region, the Brinkman-extended Darcy equations are applied to model the flow. Under the usual assumption of hydrodynamic lubrication applicable to thin films, the effects of viscous shear and the stress jump boundary condition at the porous media/fluid film interface are included in deriving the modified Reynolds equation. The effects of material properties such as coupled stress parameter viscosity ratio (_i²), thickness of porous layer (_i), permeability (K_i), and stress jump parameter (_i), on the velocity distributions and load capacities of one-dimensional converging wedge problems are discussed.