On the formulation and implementation of geometric and manufacturing constraints in node–based shape optimization

We introduce a novel method to handle geometrical and manufacturing constraints in parameter–free shape optimization. Therefore the design node coordinates are split in two sets where one set is declared as new design variables and the other set is coupled to the new design variables such that the geometrical constraint is fulfilled. Thereby no additional equations are appended to the optimization problem. In contrast the implementation of a demolding constraint is presented by formulating inequality constraints which indeed have to be attached to the optimization problem. In the context of a sensitivity–based shape optimization approach all manufacturing constraints have to be formulated in terms of the finite element node coordinates such that first order gradients with respect to the design node coordinates can be derived.     

Layout design of reinforced concrete structures using two-material topology optimization with Drucker–Prager yield constraints

This paper aims to develop a method that can automatically generate the optimal layout of reinforced concrete structures by incorporating concrete strength constraints into the two-material topology optimization formulation. The Drucker–Prager yield criterion is applied to predict the failure behavior of concrete. By using the power-law interpolation, the proposed optimization model is stated as a minimum compliance problem under the yield stress constraints on concrete elements and the material volume constraint of steel. The ε-relaxation technique is employed to prevent the stress singularity. A hybrid constraint-reduction strategy, in conjunction with the adjoint-variable sensitivity information, is integrated into a gradient-based optimization algorithm to overcome the numerical difficulties that arise from large-scale constraints. It can be concluded from numerical investigations that the proposed model is suitable for obtaining a reasonable layout which makes the best uses of the compressive strength of concrete and the tensile strength of steel. Numerical results also reveal that the hybrid constraint-reduction strategy is effective in solving the topology optimization problems involving a large number of constraints.     

Topology optimization of steady and unsteady incompressible Navier–Stokes flows driven by body forces

This paper presents the topology optimization method for the steady and unsteady incompressible Navier–Stokes flows driven by body forces, which typically include the constant force (e.g. the gravity) and the centrifugal and Coriolis forces. In the topology optimization problem, the artificial friction force with design variable interpolated porosity is added into the Navier–Stokes equations as the conventional method, and the physical body forces in the Navier–Stokes equations are penalized using the power-law approach. The topology optimization problem is analyzed by the continuous adjoint method, and solved by the finite element method in conjunction with the gradient based approach. In the numerical examples, the topology optimization of the fluidic channel, mass distribution of the flow and local velocity control are presented for the flows driven by body forces. The numerical results demonstrate that the presented method achieves the topology optimization of the flows driven by body forces robustly.     

A hybrid OC–GA approach for fast and global truss optimization with frequency constraints

The truss optimization constrained with vibration frequencies is a highly nonlinear and more computational cost problem. To speed up the convergence and obtain the global solution of this problem, a hybrid optimality criterion (OC) and genetic algorithm (GA) method for truss optimization is presented in this paper. Firstly, the OC method is developed for multiple frequency constraints. Then, the most efficient variables are identified by sensitivity analysis and modified as iteration scheme. Finally, OC method, serving as a local search operator, is integrated with GA. The numerical results verify that the hybrid method provides powerful ability in searching for more optimal solution and reducing computational effort.     

A hybrid CBO–PSO algorithm for optimal design of truss structures with dynamic constraints

The vibration domain of structures can be reduced by imposing some constraints on their natural frequencies. For this purpose optimal design of structures under frequency constraints is required which involves highly non-linear and non-convex problems. In this paper an efficient hybrid algorithm is developed for solving such optimization problems. This algorithm utilizes the recently developed colliding bodies optimization (CBO) algorithm as the main engine and uses the positive properties of the particle swarm optimization (PSO) algorithm to increase the efficiency of the CBO. The distinct feature of the present hybrid algorithm is that it requires no parameter tuning. The CBO is known for being parameter independent, and avoiding the use of the traditional penalty method to handle the constraints upholds this property. Two mathematical constrained functions taken from the literature are studied to verify the performance of the algorithm. The algorithm is then applied to optimize truss structures with frequency limitations. The numerical results demonstrate the efficiency of the presented algorithm for this class of problems.     

Topology optimization of neural networks based on a coupled genetic algorithm and particle swarm optimization techniques (c-GA–PSO-NN)

In this short paper, a coupled genetic algorithm and particle swarm optimization technique was used to supervise neural networks where the applied operators and connections of layers were tracked by genetic algorithm and numeric values of biases and weights of layers were examined by particle swarm optimization to modify the optimal network topology. The method was applied for a previously studied case, and results were analyzed. The convergence to the optimal topology was highly fast and efficient, and the obtained weights and biases revealed great reliability in reproduction of data. The optimal topology of neural networks was obtained only after seven iterations, and an average square of the correlation (R ²) of 0.9989 was obtained for the studied cases. The proposed method can be used for fast and reliable topology optimization of neural networks.

     

A stress–based approach to the optimal design of structures with unilateral behavior of material or supports

The paper presents a stress-based approach that copes with the optimal design of truss-like elastic structures in case of unilateral behavior of material or ground supports. The conventional volume-constrained minimization of compliance is coupled with a set of local stress constraints that are enforced, all over the domain or along prescribed boundaries, to control the arising of members with tension-only or compression-only strength. A Drucker–Prager failure criterion is formulated to provide a smooth approximation of the no-tension or no-compression conditions governing the stress field. A selection strategy is implemented to handle efficiently the multi-constrained formulation that is solved through mathematical programming. Benchmark examples are investigated to discuss the features of the achieved optimal designs, as compared with problems involving material and ground supports with equal behavior in tension and compression. Numerical simulations show that a limited set of constraints is needed in the first iterations to steer the solution of the energy-driven optimization towards designs accounting for the prescribed assumption of unilateral strength.     

Multiobjective trajectory optimization of the wall-building robot based on RBF–NSGA-II in an uncertain viscoelastic contact environment

To solve the problem of poor masonry quality of traditional wall-building robots in an uncertain viscoelastic contact environment while reducing energy consumption, reducing contact forces with the environment, and improving work efficiency and smoothness, a segmented multiobjective trajectory optimization method is proposed based on radial basis function (RBF) and nondominated sorting genetic algorithm II (NSGA-II). The method divides the motion trajectory into the free motion segment and the masonry segment. In the masonry segment, the compensation variable is introduced at the brick-stopping position, and the values of design variables are obtained by Latin hypercube sampling. The relationship between the objective functions and the design variables is established by using an RBF substitution model. The optimal design is carried out by the NSGA-II, and the compromise solution is obtained by using the technique for order preference by similarity to an ideal solution algorithm. On this basis, a multiobjective trajectory optimization method based on seven times nonuniform B-spline curves is proposed for the free motion segment. According to the performance indicators, such as operation efficiency, trajectory smoothness, and energy consumption, the compromise solution is again sought and obtained. Finally, the proposed trajectory optimization method is compared with the standard gate-shaped trajectory planning method. The results show that after trajectory optimization, the masonry efficiency of the wall-building robot is improved by 28.36%, and the energy consumption and trajectory smoothness are reduced by 28.68% and 93.81%, respectively. At the same time, the contact force with the environment is reduced by 12.26%, and the masonry error is reduced from 2.67 to 0.13 mm. These results can contribute to the construction of walls and improve the masonry quality of bricks while considering other performance indicators.     

Control and trajectory optimization of an aircraft’s alignment with the desired track

The synthesis of the control with the optimal trajectory length is constructed for the problem of aligning an aircraft with the desired track with the ground speed vector direction along the desired track. The solution is based on the maximum principle and involves the use of numerical methods for solving the boundary value problem and analytical investigations for determining the set of possible extremals and comparing the lengths of the trajectories when selecting the optimal one. As a result of these investigations, the switching and separation lines are determined that bound the regions in the phase space which correspond to different values of the optimal relay control.     

The contact problem in Lagrangian systems subject to bilateral and unilateral constraints,with or without sliding Coulomb’s friction: a tutorial

This work deals with the existence and uniqueness of the acceleration and contact forces for Lagrangian systems subject to bilateral and/or unilateral constraints with or without sliding Coulomb’s friction. Sliding friction is known to yield singularities in the system, such as Painlevé’s paradox. Our work aims at providing sufficient conditions on the parameters of the system so that singularities are avoided (i.e., the contact problem is at least solvable). To this end, the frictional problem is treated as a perturbation of the frictionless case. We provide explicit criteria, in the form of calculable upper bounds on the friction coefficients, under which the frictional contact problem is guaranteed to remain well-posed. Complementarity problems, variational inequalities, quadratic programs and inclusions in normal cones are central tools.     

Layout and material gradation in topology optimization of functionally graded structures: a global–local approach

By means of continuous topology optimization, this paper discusses the influence of material gradation and layout in the overall stiffness behavior of functionally graded structures. The formulation is associated to symmetry and pattern repetition constraints, including material gradation effects at both global and local levels. For instance, constraints associated with pattern repetition are applied by considering material gradation either on the global structure or locally over the specific pattern. By means of pattern repetition, we recover previous results in the literature which were obtained using homogenization and optimization of cellular materials.     

Boundary model predictive control of thin film thickness modelled by the Kuramoto–Sivashinsky equation with input and state constraints

In this work, a model modal predictive control (MMPC) strategy is proposed to stabilize the falling liquid film thickness in the vertical tubes modelled by the Kuramoto–Sivashinsky (K–S) equation in the presence of naturally present state and input constraints. The novel features of proposed synthesis is the development of an infinite dimensional PDE state representation which incorporates the exact transformation of boundary into the distributed control setting and benefits arising from the property of decoupled boundary applied input actuation and K–S PDE modal states. Furthermore, the dissipative structure of the K–S spectral operator provides the foundation for the model modal based predictive controller (MMPC) synthesis which utilizes the finite dimensional state representation to formulate the quadratic objective function while the infinite dimensional K–S PDE state constraints are appropriately defined and cast in the form of a constrained quadratic programme. Finally, we demonstrate that if feasible, the MMPC achieves stabilization of the thin film thickness and satisfies naturally present state and input constraints. Numerical simulation of the boundary applied actuation evaluates the proposed method's performance.     

Parametric appraisal and optimization in machining of CFRP composites by using TLBO (teaching–learning based optimization algorithm)

The present paper focuses on machining (turning) aspects of CFRP (epoxy) composites by using single point HSS cutting tool. The optimal setting i.e. the most favourable combination of process parameters (such as spindle speed, feed rate, depth of cut and fibre orientation angle) has been derived in view of multiple and conflicting requirements of machining performance yields viz. material removal rate, surface roughness, SR \((\hbox {R}_{\mathrm{a}})\) (of the turned product) and cutting force. This study initially derives mathematical models (objective functions) by using statistics of nonlinear regression for correlating various process parameters with respect to the output responses. In the next phase, the study utilizes a recently developed advanced optimization algorithm teaching–learning based optimization (TLBO) in order to determine the optimal machining condition for achieving satisfactory machining performances. Application potential of TLBO algorithm has been compared to that of genetic algorithm (GA). It has been observed that exploration of TLBO appears more fruitful in contrast to GA in the context of this case experimental research focused on machining of CFRP composites.     

Calculation and optimization of LaBr3–MBr (Li–Cs) phase diagrams by CALPHAD method

Phase diagram of LaBr₃–MBr (M=Li–Cs) pseudo-binary systems were reassessed by CALPHAD method with Associate Model and Redlich–Kister Model. In addition the LaBr₃–LiBr system was optimized through the application of the Quasichemical Model, and LaBr₃–RbBr system was optimized by Partially Ionic Two-sublattice Model. Optimized thermodynamic properties were compared with the data previously calculated by Quasichemical Model and Partially Ionic Two-sublattice Model as well as with experimental data. The influence of the used models for calculated thermodynamic properties has been discussed.     

A new and improved version of particle swarm optimization algorithm with global–local best parameters

This paper presents a new and improved version of particle swarm optimization algorithm (PSO) combining the global best and local best model, termed GLBest-PSO. The GLBest-PSO incorporates global–local best inertia weight (GLBest IW) with global–local best acceleration coefficient (GLBest Ac). The velocity equation of the GLBest-PSO is also simplified. The ability of the GLBest-PSO is tested with a set of bench mark problems and the results are compared with those obtained through conventional PSO (cPSO), which uses time varying inertia weight (TVIW) and acceleration coefficient (TVAC). Fine tuning variants such as mutation, cross-over and RMS variants are also included with both cPSO and GLBest-PSO to improve the performance. The simulation results clearly elucidate the advantage of the fine tuning variants, which sharpen the convergence and tune to the best solution for both cPSO and GLBest-PSO. To compare and verify the validity and effectiveness of the GLBest-PSO, a number of statistical analyses are carried out. It is also observed that the convergence speed of GLBest-PSO is considerably higher than cPSO. All the results clearly demonstrate the superiority of the GLBest-PSO.

Topological optimization of continuum structures with design-dependent surface loading – Part II: algorithm and examples for 3D problems

The problem of topology optimization of 3D structures with design-dependent loading is considered. An algorithm for generating the valid loading surface of the 3D structure is presented, constituting an extension of the algorithm for 2D structures developed in Part I of this paper on the basis of a modified isoline technique. In this way the complicated calculation of the fit of the loading surface of a 3D structure may be avoided. Since the finite element mesh is fixed in the admissible 3D design domain during the period of topology evolution, the design-dependent loading surface may intersect the elements as the design changes. Independent interpolation functions are introduced along the loading surface so that the surface integral for generating the loading on the surface of the 3D structure can be performed more efficiently and simply. The bilinear 4-node serendipity surface element is constructed to describe the variable loading surface, and this matches well with the 8-node isoparametric 3D elements which have been used for the discretization of the 3D design domain. The validity of the algorithm is verified by numerical examples for 3D problems. Results of designing with design-dependent loads and with corresponding fixed loads are presented, and some important features of the computational results are discussed.     

Maximum principle for the optimal control of an ablation-transpiration cooling system with free final time and phase constraints

This paper is concerned with an optimal control problem of an abhtion-transpiration cooling control system with Stefan-Signorini boundary condition. As the continuation of the authors＇previous paper, the Dubovits Rii-Milyutin fimctional approach is again adopted in investigation of the Pontryagin＇ s maximun principle of the system. The necessary optimality condition is presented for the problem with free final horizon and phase constraints.     

Modelling stress–strain and volume change behaviour of unsaturated soils using an evolutionary based data mining technique,an incremental approach

Modelling of unsaturated soils has been the subject of many research works in the past few decades. A number of constitutive models have been developed to describe the complex behaviour of unsaturated soils. However, many have proven to be unable to predict all aspects of the behaviour of unsaturated soils in a unified manner. In this paper an alternative new approach is presented, based on the Evolutionary Polynomial Regression (EPR) technique. EPR is a data mining technique that generates a transparent and structured representation of the behaviour of a system directly from input test data. The capabilities of the proposed EPR-based framework in modelling of behaviour of unsaturated soils are illustrated using results from a comprehensive set of triaxial tests on samples of compacted unsaturated soils from literature. The main parameters used for modelling of the behaviour of unsaturated soils during shearing are initial water content, initial dry density, mean net stress, axial strain, suction, volumetric strain, and deviator stress. The model developed is used to predict different aspects of the behaviour of unsaturated soils for conditions not used in the model building process. The results show that the proposed approach provides a useful framework for modelling of unsaturated soils. The merits and advantages of the proposed approach are highlighted.     

The impact of an employee’s psychological contract breach on compliance with information security policies: intrinsic and extrinsic motivation

Cognition, Technology & Work - Despite the rapid rise in social engineering attacks, not all employees are as compliant with information security policies (ISPs) to the extent that...