Research Publications (Engineering and Built Environment)

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A procedure to select the best material combinations and optimally design hybrid composite plates for minimum weight and cost
(Taylor & Francis, 1997) Walker, Mark; Reiss, Talmon; Adali, Sarp
The optimal layup with least weight or cost for a symmetrically laminated plate subject to a buckling load is determined using a hybrid composite construction. A hybrid construction provides further tailoring capabilities and can meet the weight, cost and strength constraints while a non-hybrid construction may fail to satisfy the design requirements. The objective of the optimization is to minimize either the weight or cost of the plate using the ply angles, layer thicknesses and material combinations as design variables. As the optimization problem contains a large number of continuous (ply angles and thicknesses) and discrete (material combinations) design variables, a -sequential solution procedure is devised in which the optimal variables are computed in different stages. The proposed design method is illustrated using graphite, kevlar and glass epoxy combinations and the efficiencies of the hybrid designs over the non-hybrid ones are computed.
Optimal design of symmetrically laminated plates for minimum deflection and weight
(Elsevier, 1997) Walker, Mark; Reiss, Talmon; Adali, Sarp
The minimum deflection and weight designs of laminated composite plates are given. The finite element method using Mindlin plate theory is used in conjunction with optimisation routines in order to obtain the optimal designs. Various boundary conditions are considered and results are given for varying aspect ratios and for different loading types. Comparative results are presented for minimum weight priority design as an alternative to minimum deflection/minimum weight priority design to investigate the effect of priority on the deflection and weight.
A technique for the multiobjective optimisation of laminated composite structures using genetic algorithms and finite element analysis
(Elsevier, 2003) Walker, Mark; Smith, Ryan E.
A methodology for using genetic algorithms with the finite element method to minimise a weighted sum of the mass and deflection of fibre reinforced structures with several design variables is described. The design constraint implemented is based on the Tsai–Wu failure criterion. Symmetrically laminated composite rectangular plates with eight layers are used to demonstrate the technique. Thus, the four fibre orientations and laminae thicknesses are to be determined optimally by defining a design index comprising a weighted average of the objective functions and determining the minimum. In addition, the fibre orientations and layer thicknesses must be selected from a set of discrete values. Results are presented for different load distributions, and various combinations of clamped, simply supported and free boundary conditions. The effect of aspect ratio on the results is also investigated.
A technique for optimally designing fibre-reinforced laminated plates with manufacturing uncertainties for maximum buckling strength
(Taylor & Francis, 2005) Walker, Mark; Hamilton, Ryan Jason
This article describes a procedure to design symmetrically laminated plates for maximum buckling load with manufacturing uncertainty in the ply angle, which is the design variable. It is assumed that the probability of any tolerance value occurring within the tolerance band, compared with any other, is equal. The methodology is flexible enough to allow any appropriate problem formulation and search algorithm to be substituted. Three different tolerance scenarios are used for the purposes of illustrating the methodology, and plates with varying aspect ratios and loading ratios are optimally designed and compared.
Minimum weight design of composite hybrid shells via symbolic computation
(Elsevier, 1997) Walker, Mark; Reiss, Talmon; Adali, Sarp
The best layup for a hybrid laminated cylindrical shell subject to a buckling load constraint is determined. The objective of the optimisation is the minimum weight design of these structures. The ply angle is taken as the design variable. Various configurations of graphite and boron epoxy layers are considered in order to determine an optimal stacking sequence. The symbolic computational software package MATHEMATICA is used in the implementation and solution of the problem. This approach simplifies the computational procedure as well as the implementation of the analysisloptimisation routine. Results are given illustrating the dependence of the optimal layup on the cylinder length and radius. It is shown that a general purpose computer algebra system like MATHEMATICA is well suited to solve structural design problems involving composite materials.
A static shape control model for piezo-elastic composite structures
(Elsevier, 2003) Kekana, Marino
This study examines an active control model in which the open circuit mode is assumed. A finite element model in which only the displacement field is approximated is developed. The charge–potential relationship is incorporated into the finite element model. This results in a model for controlling the shape of a piezo-elastic structure. This model is then used to simulate a structure in the active control mode at zero amplifier gain. Results show that piezo-electric control forces persist at zero amplifier gain. Also, a structure in the active control mode at zero amplifier gain is shown to be stiffer than it is in the passive mode. This implies that piezo-electric control forces persisting at zero amplifier gain have a significant contribution in the analysis when this control model is used.
A technique for optimally designing engineering structures with manufacturing tolerances accounted for
(Taylor & Francis, 2007) Tabakov, Pavel Y.; Walker, Mark
Accurate optimal design solutions for most engineering structures present considerable difficulties due to the complexity and multi-modality of the functional design space. The situation is made even more complex when potential manufacturing tolerances must be accounted for in the optimizing process. The present study provides an in-depth analysis of the problem, and then a technique for determining the optimal design of engineering structures, with manufacturing tolerances in the design variables accounted for, is proposed and demonstrated. The examples used to demonstrate the technique involve the design optimization of simple fibre-reinforced laminated composite structures. The technique is simple, easy to implement and, at the same time, very efficient. It is assumed that the probability of any tolerance value occurring within the tolerance band, compared with any other, is equal, and thus it is a worst-case scenario approach. In addition, the technique is non-probabilistic. A genetic algorithm with fitness sharing, including a micro-genetic algorithm, has been found to be very suitable to use, and implemented in the technique. The numerical examples presented in the article deal with buckling load design optimization of an laminated angle ply plate, and evaluation of the maximum burst pressure in a thick laminated anisotropic pressure vessel. Both examples clearly demonstrate the impact of manufacturing tolerances on the overall performance of a structure and emphasize the importance of accounting for such tolerances in the design optimization phase. This is particularly true of the pressure vessel. The results show that when the example tolerances are accounted for, the maximum design pressure is reduced by 60.2% (in the case of a single layer vessel), and when five layers are specified, if the nominal fibre orientations are implemented and the example tolerances are incurred during fabrication, the actual design pressure could be 64% less than predicted.
A methodology for optimally designing fibre-reinforced laminated structures with design variable tolerances for maximum buckling strength
(Elsevier, 2005) Walker, Mark; Hamilton, Ryan Jason
A procedure to design symmetrically laminated structures for maximum buckling load with manufacturing uncertainty in the ply angle—which is the design variable, is described. It is assumed that the probability of any tolerance value occurring within the tolerance band, compared with any other, is equal, and thus the technique is aimed at designing for the worst-case scenario. The finite element method is implemented and used to determine the fitness of each design candidate, and so the effects of bending–twisting coupling are accounted for. The methodology is flexible enough to allow any appropriate finite element formulation and search algorithm to be substituted. Three different tolerance scenarios are used for the purposes of illustrating the methodology, and plates with varying aspect and loading ratios, as well as differing boundary conditions, are chosen to demonstrate the technique, and optimally designed and compared.
Optimal design of symmetric angle-ply laminates subject to nonuniform buckling loads and in-plane restraints
(Elsevier, 1996) Walker, Mark; Adali, Sarp; Verijenko, Viktor E.
Optimal buckling designs of symmetrically laminated rectangular plates under in-plane uniaxial loads" which have a nonuniform distribution along the edges are presented. In particular, point loads, partial uniJorm loads and nonuniform loads" are considered in addition to uniform O' distributed inplane loads" which provide the benchmark solutions. Poisson's effect is" taken into account when in-plane restraints are present along the unloaded edges. Restraints give rise to in-plane loads" at unloaded edges which lead to biaxial loading, and may cause premature instability. The laminate behaviour with respect to fiber orientation changes significantly in the presence of Poisson's eJfi, ct as compared to that o/'a laminate where this" ~Jfect is neglected. This change in behaviour has significant implications Jor design optimisation as the optimal values of design variables with or without restraints differ substantially. In the present study, the design objective is" the maximisation of the uniaxial buckling load by optimally determining the fiber orientations. The )qnite element method, coupled with an optimisation routine, is employed in analysing and optimising the laminates. Numerical results are given for a number of boundary conditions and fi)r uniJormly and non-uniformly distributed buckling loads.
Optimal design of symmetrically laminated plates for maximum buckling temperature
(Taylor & Francis, 1997) Walker, Mark; Reiss, Talmon; Adali, Sarp; Verijenko, Viktor E.
The optimal designs of laminated plates subject to nonuniform temperature distributions are givenfor maximum bucklingtemperature. The method ofsolution involves the finite element method based on Mindlin plate theory and numerical optimization: A computational approach is developed that involves successive stages of solution for temperature distribution, buckling temperature, and optimalfiber angle. Three different temperature loadingsare consideredand various combinations of simply supported and clamped boundary conditionsare studied. The effectofplate aspectratioon the optimal fiber angle and the maximum buckling temperature is investigated. The influence of bending-twisting coupling on the optimum design is studied by considering plates with an increasing number of layers.
Correlation between elastic and electric properties for cyclically loaded metals
(Springer, 2002) Sevostianov, Igor; Bogarapu, Mahesh; Tabakov, Pavel Y.
A new method of evaluation of the elastic property deterioration due to accumulated damage is suggested and experimentally verified. It is based on the explicit correlations between two groups of anisotropic properties – conductivity and elasticity, recently established for porous/microcracked materials with anistropic microstructures. An experimental study of fatigue has been done to verify the theoretical predictions. The electrical resistance and Young''s modulus are measured as functions of the number of loading cycles in the standard fatigue tests. The agreement between the theoretical predictions and the direct experimental data is better than 10% in all cases. The results allow one to use measurements of the electric resistance to estimate the damage accumulated in methal structures and the decrease of the elastic modulus.
Lay-up optimization of multilayered anisotropic cylinders based on a 3-D elasticity solution
(Elsevier, 2006) Tabakov, Pavel Y.; Summers, E. B.
Exact elasticity solutions are obtained using the stress function approach, where the radial, circumferential and shear stresses are determined, taking into account the closed ends of the cylindrical shell. The system of the governing algebraic equations is derived to accurately analyse a multilayered pressure vessel with an arbitrary number of layers and any thickness. The approach used is straight-forward compared to other three-dimensional solutions found in the literature. The design of multilayered composite pressure vessels is accomplished using the genetic algorithm and subject to the Tsai–Wu failure criterion. The genetic algorithm is optimized to serve this particular problem
Refined theory of laminated anisotropic shells for the solution of thermal stress problems
(Taylor & Francis, 1999) Verijenko, Viktor E.; Tauchert, T. R.; Shaikh, C.; Tabakov, Pavel Y.
A new higher order theory of laminated anisotropic shells for the solution of thermal stress problems that takes into account transverse shear stresses is developed.The theory is based on the kinematic hypotheses that were not assumed a priori but derived on the basis of an iterative technique. The hypotheses take into account the influence of the tangential components of the external loads and the temperature on distributions of the transverse shear stresses through the thickness of the shell. Some analytical solutions are obtained on the basis of the theory developed, and the results are compared with those available in the literature. The theory is also implemented on the basis of the finite element method, and a new triangular finite element is formulated. Some numerical results on the basis of this finite element are also presented.
Stress distribution in continuously heterogeneous thick laminated pressure vessels
(Elsevier, 2001) Verijenko, Viktor E.; Adali, Sarp; Tabakov, Pavel Y.
Stress analysis of multilayered pressure vessels possessing cylindrical anisotropy and under internal, external and interlaminar pressures is given. The special case when the axis of anisotropy coincides with the axis of symmetry Oz and the stresses do not vary along the generator is investigated. In this case there exists a plane of elastic symmetry normal to this axis at every point of the cylinder so that each layer may be considered as orthotropic. However, elastic properties can vary through the thickness of a layer. Exact elasticity solutions are obtained for both open-ended and closed-ended cylinders using a stress function approach. The method of solution allows the forces on the layer interfaces to be taken into account with relative ease. Numerical results are presented for thick cylinders with isotropic and orthotropic layers, and stress distributions across the thickness are shown.
Multi-dimensional design optimisation of laminated structures using an improved genetic algorithm
(2001) Tabakov, Pavel Y.
The present study demonstrates a new variation of the genetic algorithm (GA) technique for engineering applications. This approach is highly efficient for many classes of engineering problems. The proposed selection of the best individuals and localised search makes the search more effective and rapidly improves the fitness value from generation to generation. Both continuous and discrete design variables are considered, and a comparative analysis of the performance of the algorithm is studied. The evaluation of the burst pressure of thick composite pressure vessels based on three-dimensional stress–strain analysis is considered here as an example. Exact elasticity solutions are obtained using the stress function approach where the radial, circumferential and shear stresses are determined taking the closed ends of the cylindrical shell into account.
Optimization of symmetric laminates for maximum buckling load including the effects of bending-twisting coupling
(Elsevier, 1996) Walker, Mark; Adali, Sarp; Verijenko, Viktor E.
Finite element solutions are presented for the optimal design of symmetrically laminated rectangular plates subjected to a combination of simply supported, clamped and free boundary conditions. The design objective is the maximization of the biaxial buckling load by determining the fibre orientations optimally, with the effects of bending-twisting coupling taken into account. The finite element method coupled with an optimization routine is employed in analysing and optimizing the laminated plate designs. The effects of boundary conditions, the number of layers and bending-twisting coupling on the optimal ply angles and the buckling load are numerically studied.
Multiobjective optimization of laminated plates for maximum prebuckling, buckling and postbuckling strength using continuous and discrete ply angles
(Elsevier., 1996) Adali, Sarp; Walker, Mark; Verijenko, Viktor E.
The optimal design of uniaxially loaded laminated plates subject to elastic in-plane restraints along the unloaded edges are given for a maximum combination of prebuckling stiffness, postbuckling stiffness and buckling load. The results are also obtained for biaxially loaded plates without elastic restraints. The method of solution involves defining a design index comprising a weighted average of the objective functions and identifying candidate configurations which have to be optimized and compared to determine the best stacking sequence. This multiobjective approach leads to improved prebuckling, buckling and postbuckling performance. A similar approach is adopted in the case of discrete ply angles with the provision that these angles can only take predefined values. From a manufacturing viewpoint, using only certain fibre orientations such as 0, ± 45 and 90 ° is advantageous and cost-effective. The multiobjective design results are compared to single objective ones, and the effect of various problem parameters on the optimal designs are numerically studied. It is observed that the resulting trade-off among the different objectives are not severe leading to well-balanced laminates with regard to the range of loads they are required to carry. A comparison of continuous and discrete optimization indicates that both designs lead to comparable load carrying capacity, with regard to different objectives
Multiobjective design of laminated plates for maximum stability using the finite element method
(Elsevier, 2001) Walker, Mark
Finite element solutions are presented for the optimal multiobjective design of symmetrically laminated rectangular plates subject to a combination of simply supported, clamped and free boundary conditions. The design objective is the maximisation of the biaxial buckling load and resonance frequency by determining the fibre orientation optimally with the effects of bending–twisting coupling taken into account. The finite element method coupled with an optimisation routine is employed in analysing and optimising the laminated plate designs. The effect of boundary conditions and bending–twisting coupling on the optimal ply angles and the buckling load are numerically studied. In addition, the multiobjective results are also compared to single objective design results
A technique for stiffness improvement by optimization of fiber steering in composite plates
(Springer, 2010) Tabakov, Pavel Y.; Walker, Mark
A methodology for stiffness improvement by optimal orientation of fibers placed using fiber steering techniques of composite plates has been developed and is described here. A genetic algorithm is employed to determine the optimal orientation of the tow fibers and, in addition, once the plate has been divided up into cells in order to apply the technique, the orientation gradient between adjacent cells is capped. The finite element method (FEM) is used to determine the fitness of each design candidate. The approach developed also differs from existing ones by having a more sophisticated chromosome string. By relying on the algorithm for the calculation of the fiber orientation in a specific cell, a relatively short and rapid convergence string is assembled. The numerical results obtained show a significant improvement in stiffness when the fiber orientation angle is allowed to vary spatially throughout the ply.
Optimal design of symmetric laminates with cut-outs for maximum buckling load
(Elsevier, 1999) Walker, Mark
Finite element solutions are presented for the optimal design of symmetrically laminated rectangular plates with central circular cut-outs subject to a combination of simply supported, clamped and free boundary conditions. The design objective is the maximisation of the biaxial buckling load by determining the fibre orientations optimally with the effects of bending–twisting coupling taken into account. The finite element method coupled with an optimisation routine is employed in analysing and optimising the laminated plate designs. The effect of plate size and boundary conditions on the optimal ply angles and the buckling load are numerically studied, and these results are compared to those from an article which appeared in this journal in 1996; viz. plates without cut-outs (Walker M, Adali S, Verijenko VE. Optimisation of symmetric laminates for maximum buckling load including the effects of bending–twisting coupling.