Structural Optimization Procedure Research Articles

Designing and optimization of new composite pallet

The original code KEDRO for design of experiments, analysis and multiobjective robust optimization is used for designing of a new composite pallet. Firstly code is tested for non-deterministic optimization of the two bar truss problem. Then robust optimization problem of composite pallet is solved. The FE-model of the composite pallet is considered and solved accurately as multi-ply shell structure. The fiber-reinforced polymer material mechanical properties and two main operation cases of the loaded pallet are taken into account during deterministic structural optimization procedure. Next, the same problem is considered as non-deterministic taking into account possible uncertainties of the pallet supporting conditions. In both cases shape is defined using CAD based NURBS curves. Appropriate shapes of the stiffness ribs are found for best performance of the structure. As a result of optimization, the competitive design of composite pallet is developed.

Structural shape optimization of free-form surface shell and property of solution search using firefly algorithm

The computation procedure for structural shape optimization is based on the heuristic optimization procedures, such as swarm intelligence (SI), that use patterns found in self-organizing phenomena observed in nature. Most SI techniques including particle swarm optimization (PSO) and artificial bee colony (ABC), attain a global optimal solution. The firefly algorithm (FA) can attain both a global optimal and local optimal solutions by setting suitable computational parameters. However, the method for setting these parameters is comparatively difficult. In order to simplify the setting of these parameters, we implement a computational scheme where the distance between two fireflies in the design variable space is dimensionless. The effectiveness and the validity of this FA are clarified by showing the diversified solution for a global optimal solution and local optimal solutions using a local search in the structural shape optimization of a free-form surface shell.

Robust optimum design of base isolation system in seismic vibration control of structures under random system parameters

The optimum design of base isolation system to control seismic vibration considering uncertain system parameters are usually performed by minimizing the unconditional expected value of mean square response of a structure without any consideration to the variance of such responses due to system parameter uncertainty. However, the unconditional mean square response based designed may have larger variance of responses due to uncertainty in system parameters and the overall system performance may be sensitive. But, it is desirable that the optimum design should reduce both the mean and variance of dynamic performance measure under system parameter uncertainty. The present study deals with robust design optimization (RDO) of base isolation system considering random system parameters characterizing the structure, isolator and ground motion model. The RDO is performed by minimizing the weighted sum of the expected value of the maximum root mean square acceleration of the structure as well its standard deviation. A numerical study elucidates the importance of the RDO procedure for design of base isolation system by comparing the proposed RDO results with the results obtained by the conventional stochastic structural optimization procedure and the unconditional response based optimization.

Robust design of liquid column vibration absorber in seismic vibration mitigation considering random system parameter

The optimum design of liquid column dampers in seismic vibration control considering system parameter uncertainty is usually performed by minimizing the unconditional response of a structure without any consideration to the variation of damper performance due to uncertainty. However, the system so designed may be sensitive to the variations of input system parameters due to uncertainty. The present study is concerned with robust design optimization (RDO) of liquid column vibration absorber (LCVA) considering random system parameters characterizing the primary structure and ground motion model. The RDO is obtained by minimizing the weighted sum of the mean value of the root mean square displacement of the primary structure as well as its standard deviation. A numerical study elucidates the importance of the RDO procedure for design of LCVA system by comparing the RDO results with the results obtained by the conventional stochastic structural optimization procedure and the unconditional response based optimization.

A Novel Fluid Structure Interaction-EHD Model and Optimization Procedure for an Asymmetrical Axially Balanced External Gear Machine

This article presents a novel fluid structure interaction (FSI) model for lateral lubricating interfaces in an asymmetrically balanced external gear pump. Due to the asymmetry in the geometry of the floating lateral bushes responsible for sealing the displacement chambers in such machines, the lubricating interfaces on either side of the gears have been modeled as distinct but coupled lubricating films. An elastohydrodynamic (EHD) lubrication regime was modeled in all simulations and film thickness predictions for both lubricating interfaces have been achieved. The novel FSI model for the asymmetric lateral gaps is then used in an automatic optimization procedure to design the optimal axial balance in the reference external gear machine (EGM). The optimal axial balance is achieved by determining the optimal balance area on the lateral bush by considering specific design variables associated with it. The procedure aims to find the best feasible design solution that minimizes the total power losses in the lubricating interfaces while also minimizing the nonuniformities in the orientation of these gaps between two significant operating conditions of the EGM. The developed procedure highlights the potential to virtually design the axial balance in EGMs—which represent a key design aspect of pressure compensated EGM—by using an advanced FSI-EHD model.

Electromagnetic band-gap structure design using the auxetic unit-structure for easily controllable tunability

Tunable electromagnetic band-gap structures for matching an intended band-gap range have more potential for various applications than ordinary electromagnetic band-gap structures with a fixed or non-linearly variable band-gap range. However, there has not been much progress on the study of the appropriate shape of the structure. To obtain a controllable and tunable electromagnetic band-gap, we propose a new design concept employing a unit-structure with a negative Poisson's ratio close to −1 to realize an approximately linear band-gap shift according to the variation of the shape of the structure. We used a structural optimization procedure based on the phase field method to obtain the design of the unit-structure. We investigated the relation between the auxetic unit-structure deformation and the change in the band-gap range through numerical simulations and also evaluated the possibility to realize the design experimentally in the radio frequency range.

Combining Structure and Parameter Adaptation of HMMs for Printed Text Recognition.

We present two algorithms that extend existing HMM parameter adaptation algorithms (MAP and MLLR) by adapting the HMM structure. This improvement relies on a smart combination of MAP and MLLR with a structure optimization procedure. Our algorithms are semi-supervised: to adapt a given HMM model on new data, they require little labeled data for parameter adaptation and a moderate amount of unlabeled data to estimate the criteria used for HMM structure optimization. Structure optimization is based on state splitting and state merging operations and proceeds so as to optimize either the likelihood or a heuristic criterion. Our algorithms are successfully applied to the recognition of printed characters by adapting the HMM character models of a polyfont printed text recognizer to new fonts. Our experiments involve a total of 1,120,000 real and 3,100,000 synthetic character images and concern a set of 89 HMM models. A comparison of our results with those of state-of-the-art adaptation algorithms (MAP and MLLR) shows a significant increase in the accuracy of character recognition.

Optimum design methodologies for pile foundations in London

Given the importance of pile foundations in geotechnical engineering for supporting high-significance structures such as bridges, high-rise buildings, power plant stations, offshore platforms and museums, it becomes a necessity to find the best pile foundation design in terms of performance and economy. The number of piles required might exceed several hundreds or even thousands while the pile foundation cost might exceed 20% of the construction cost of the superstructure. In this work the problem of finding optimized designs of pile foundations is examined and is performed in accordance to two design code recommendations, namely Eurocode 7 and DIN 4014. The proposed structural optimization procedure is implemented in two real-world cases both located in London, UK in order to assess the efficiency of the proposed design formulation.

A smooth evolutionary structural optimization procedure applied to plane stress problem

Topological optimization problems based on stress criteria are solved using two techniques in this paper. The first technique is the conventional Evolutionary Structural Optimization (ESO), which is known as hard kill, because the material is discretely removed; that is, the elements under low stress that are being inefficiently utilized have their constitutive matrix has suddenly reduced. The second technique, proposed in a previous paper, is a variant of the ESO procedure and is called Smooth ESO (SESO), which is based on the philosophy that if an element is not really necessary for the structure, its contribution to the structural stiffness will gradually diminish until it no longer influences the structure; its removal is thus performed smoothly. This procedure is known as “soft-kill”; that is, not all of the elements removed from the structure using the ESO criterion are discarded. Thus, the elements returned to the structure must provide a good conditioning system that will be resolved in the next iteration, and they are considered important to the optimization process. To evaluate elasticity problems numerically, finite element analysis is applied, but instead of using conventional quadrilateral finite elements, a plane–stress triangular finite element was implemented with high-order modes for solving complex geometric problems. A number of typical examples demonstrate that the proposed approach is effective for solving problems of bi-dimensional elasticity.

Revisiting approximate reanalysis in topology optimization: on the advantages of recycled preconditioning in a minimum weight procedure

An efficient procedure for three-dimensional continuum structural topology optimization is proposed. The approach is based on recycled preconditioning, where multigrid preconditioners are generated only at selected design cycles and re-used in subsequent cycles. Building upon knowledge regarding approximate reanalysis, it is shown that integrating recycled preconditioning into a minimum weight problem formulation can lead to a more efficient procedure than the common minimum compliance approach. Implemented in MATLAB, the run time is roughly twice faster than that of standard minimum compliance procedures. Computational savings are achieved without any compromise on the quality of the results in terms of the compliance-to-weight trade-off achieved. This provides a step towards integrating interactive 3-D topology optimization procedures into CAD software and mobile applications. MATLAB codes complementing the article can be downloaded from the author's personal webpage.

First-principles quantum molecular dynamics study of TixZr1−xN(111)/SiNy heterostructures and comparison with experimental results

The heterostructures of five monolayers B1–TixZr1−xN(111), x = 1.0, 0.6, 0.4 and 0.0 (where B1 is a NaCl-type structure) with one monolayer of a Si3N4-like Si2N3 interfacial layer were investigated by means of first-principles quantum molecular dynamics and a structure optimization procedure using the Quantum ESPRESSO code. Slabs consisting of stoichiometric TiN and ZrN and random, as well as segregated, B1–TixZr1−xN(111) solutions were considered. The calculations of the B1–TixZr1−xN solid solutions, as well as of the heterostructures, showed that the pseudo-binary TiN–ZrN system exhibits a miscibility gap. The segregated heterostructures in which Zr atoms surround the SiyNz interface were found to be the most stable. For the Zr-rich heterostructures, the total energy of the random solid solution was lower compared to that of the segregated one, whereas for the Ti-rich heterostructures the opposite tendency was observed. Hard and super hard Zr–Ti–Si–N coatings with thicknesses from 2.8 to 3.5 μm were obtained using a vacuum arc source with high frequency stimulation. The samples were annealed in a vacuum and in air at 1200 °C. Experimental investigations of Zr–Ti–N, Zr–Ti–Si–N and Ti–Si–N coatings with different Zr, Ti and Si concentrations were carried out for comparison with results obtained from TixZr1−xN(111)/SiNy systems. During annealing, the hardness of the best series samples was increased from (39.6 ± 1.4) to 53.6 GPa, which seemed to indicate that a spinodal segregation along grain interfaces was finished. A maximum hardness of 40.8 GPa before and 55 GPa after annealing in air at 500 °C was observed for coatings with a concentration of elements of Si  (7–8) at.%, Ti  22 at.% and Zr  70 at.%.

The periodic resin configuration design for ceramic-resin composite structure using topology optimization

The ceramic-resin composite structure has broad prospects in many fields like rapid casting and thermal protection. Due to the coefficient of thermal expansion (CTE) of resin is about 10 times higher than that of ceramic, the excessive thermal expansion of the resin pattern will lead to the undesirable crack of the ceramic shell during the heating procedure. The proposed approach is to find a reasonable resin configuration minimizing the thermal stress in the ceramic shell. Simultaneously, the mechanical stiffness of the whole structure should be maintained at a certain level to resist the pressure applied on the ceramic shell. In the actual production, the periodic resin configurations are more operable than the disordered configuration, so finding reasonable periodic resin configurations for ceramic-resin composite structure has lots of significance. The purpose of this paper is to introduce the topology optimization method into the periodic resin configuration design for ceramic-resin composite structure. A structural topology optimization procedure in combination with thermo-mechanical finite element analysis has been developed. A single-layer periodic model and a double-layer periodic model are optimized and respective CAD models are rebuilt according to the optimal results. By comparing with the existing hexagonal honeycomb configuration, two optimal designs have shown better performances both in reducing the thermal stress in the ceramic shell and maintaining the stiffness of the whole structure.

Structural optimization procedure of a composite wind turbine blade for reducing both material cost and blade weight

A composite blade structure for a 2 MW horizontal axis wind turbine is optimally designed. Design requirements are simultaneously minimizing material cost and blade weight while satisfying the constraints on stress ratio, tip deflection, fatigue life and laminate layup requirements. The stress ratio and tip deflection under extreme gust loads and the fatigue life under a stochastic normal wind load are evaluated. A blade element wind load model is proposed to explain the wind pressure difference due to blade height change during rotor rotation. For fatigue life evaluation, the stress result of an implicit nonlinear dynamic analysis under a time-varying fluctuating wind is converted to the histograms of mean and amplitude of maximum stress ratio using the rainflow counting algorithm Miner's rule is employed to predict the fatigue life. After integrating and automating the whole analysis procedure an evolutionary algorithm is used to solve the discrete optimization problem.

Structure Design of Stamping Die Based on Topology Optimization and Shape Optimization

To quantitatively analyze the structural topology and control the elastic deformation of die structure in stamping, a new die structure design method was proposed. The forming analysis was conducted based on the die surface mesh generated in the third-party software. Structural analysis models were established according to the die surface mesh and deformation resistance obtained from forming analysis results. And then, the structure analysis and optimization were carried out. This new method for structure design of stamping die has two advantages. First one is the combination of forming analysis and structure analysis makes the structural optimization procedure more practical. Secondly, the coupling of topology optimization and shape optimization makes it possible to fundamentally change the structural topology and it is a new attempt to mold design.

β-Mn-Type Co8+xZn12–x as a Defect Cubic Laves Phase: Site Preferences, Magnetism, and Electronic Structure

The results of crystallographic analysis, magnetic characterization, and theoretical assessment of β-Mn-type Co-Zn intermetallics prepared using high-temperature methods are presented. These β-Mn Co-Zn phases crystallize in the space group P4(1)32 [Pearson symbol cP20; a = 6.3555(7)-6.3220(7)], and their stoichiometry may be expressed as Co(8+x)Zn(12-x) [1.7(2) < x < 2.2(2)]. According to a combination of single-crystal X-ray diffraction, neutron powder diffraction, and scanning electron microscopy, atomic site occupancies establish clear preferences for Co atoms in the 8c sites and Zn atoms in the 12d sites, with all additional Co atoms replacing some Zn atoms, a result that can be rationalized by electronic structure calculations. Magnetic measurements and neutron powder diffraction of an equimolar Co:Zn sample confirm ferromagnetism in this phase with a Curie temperature of ∼420 K. Neutron powder diffraction and electronic structure calculations using the local spin density approximation indicate that the spontaneous magnetization of this phase arises exclusively from local moments at the Co atoms. Inspection of the atomic arrangements of Co(8+x)Zn(12-x) reveals that the β-Mn aristotype may be derived from an ordered defect, cubic Laves phase (MgCu2-type) structure. Structural optimization procedures using the Vienna ab initio simulation package (VASP) and starting from the undistorted, defect Laves phase structure achieved energy minimization at the observed β-Mn structure type, a result that offers greater insight into the β-Mn structure type and establishes a closer relationship with the corresponding α-Mn structure (cI58).

Optimization of bearing structure of ballast leveling machine SPZ-5/UA

Purpose. The results of the optimization investigation and the rational projects of the bearing structure of ballast leveling machine SPZ-5/UA are brought in this paper. The necessity of realization of structural optimization of the investigated machine is reasonable. Methodology. The statement of the optimization problem is executed: the beam cross-section square is taken as the objective function; the allowable stresses criterion is taken as the constraint in this problem statement. Findings. The simplified FE-model of structure of machine is worked out. The optimization problem of double-T cross-section is considered as a test case. For this problem we can obtain the analytical and numeral solutions. Originality. The rational designs for the bearing structure of the investigated machine are brought with the increased consumption of material with preservation of durability characteristics. Practical value. The optimization investigation is executed for bearing structure of the ballast leveling machine SPZ-5/UA by the use of the numerical structural optimization procedure. The obtained rational structural projects are compared to the structural projects with standard double-T cross-sections. It is shown that the use of structural projects with standard cross-sections makes it impossible to obtain the better structure as compared to the rational project. As a result the rational structural project of the ballast leveling machine is obtained, which have the sufficient safety factor. The cross-section of the main longitudinal beam of the bearing structure of leveling machine is decreased on 73%.

An efficient approach for the assembly of mass and stiffness matrices of structures with modifications

The finite element method is one of the most common tools for the comprehensive analysis of structures with applications reaching from static, often nonlinear stress–strain, to transient dynamic analyses. For single calculations the expense to generate an appropriate mesh is often insignificant compared to the analysis time even for complex geometries and therefore negligible. However, this is not the case for certain other applications, most notably structural optimization procedures, where the (re-)meshing effort is very important with respect to the total runtime of the procedure. Thus it is desirable to find methods to efficiently generate mass and stiffness matrices allowing to reduce this effort, especially for structures with modifications of minor complexity, e.g. panels with cutouts.Therefore, a modeling approach referred to as Energy Modification Method is proposed in this paper. The underlying idea is to model and discretize the basis structure, e.g. a plate, and the modifications, e.g. holes, separately. The discretized energy expressions of the modifications are then subtracted from (or added to) the energy expressions of the basis structure and the coordinates are related to each other by kinematical constraints leading to the mass and stiffness matrices of the complete structure. This approach will be demonstrated by two simple examples, a rod with varying material properties and a rectangular plate with a rectangular or circular hole, using a finite element discretization as basis. Convergence studies of the method based on the latter example follow demonstrating the rapid convergence and efficiency of the method. Finally, the Energy Modification Method is successfully used in the structural optimization of a circular plate with holes, with the objective to split all its double eigenfrequencies.

SHAPE OPTIMIZATION OF UNDERGROUND EXCAVATION BY SIMULATED ANNEALING

Abstract The paper deals with the problem of shape optimization of underground tunnel excavation. In the pioneering work of Sałustowicz, the elliptic shape was assumed a priori to be an optimal one and then a determination of suitable semi-axes ratio was only the question. Two cases were distinguished there: self-supporting excavation and excavation with the structural support. An evolutionary structural optimization (ESO) procedure, employed in 2005 to optimize shape of underground excavation, confirms the assumptions concerning the case of self-supporting excavations. The case of supported excavation is considered in the present work. Optimization procedure of the simulated annealing (SA) is incorporated in the study. An energetic optimality condition, formulated in the authors’ previous papers is also adopted. Itasca FLAC software is utilized in numerical examples. Four different in situ stress ratios are investigated. The numerical results obtained confirm that the optimal shape tends to be an ellipse. The semi-axes ratio demonstrates compliance with the assumptions already existing in literature.

Design and fabrication of biphasic cellular materials with transport properties – A modified bidirectional evolutionary structural optimization procedure and MATLAB program

Heat and mass transfer in macellular materials signifies an important topic of research for a range of advanced applications such as in thermal, aerospace, geotechnical and scaffold tissue engineering etc. Based on the mathematical similarity of various transport problems, this paper proposes a modified bidirectional evolutionary structural optimization (BESO) method for design of biphasic microstructural composites with desirable transport properties. The cellular materials considered herein comprise periodic base cells and the homogenization technique is adopted to determine their effective (bulk) properties. The key is to optimize the topology of base cell model for minimizing the difference between the effective and target transport properties. Numerical examples agree well with the well-known benchmarking microstructures and some of them are prototyped using biphasic solid free-form fabrication (SFF) technology. To facilitate comprehension of the algorithm, a short MATLAB program is provided in the Appendix.

The lattice structure configuration design for stereolithography investment casting pattern using topology optimization

PurposeThe purpose of this paper is to introduce, for the first time, the topology optimization method into the lattice structure configuration design for rapid casting patterns.Design/methodology/approachA structural topology optimization procedure in combination with thermo‐mechanical finite element analysis for the lattice structure configuration design has been developed.FindingsA new mixed stress‐compliance optimization model is proposed for the strength and rigidity design. Numerical modeling about the mathematical formulation of the objective function and design constraints is established and an optimal material layout inside a given domain of the stereolithography (SL) resin pattern is found.Originality/valueVarious optimal results of lattice structure configurations are obtained numerically. By comparing the optimal designs with the existing lattice structure configurations, the newly obtained designs have shown better performances both in reducing the stress in the ceramic shell and in maintaining the stiffness of the SL pattern.