Reddy's Theory Research Articles

Behavior of Functionally Graded Porous Plate in Bending with Smoothed Element

The bending analysis of functionally graded porous (FGP) plates using a four-node quadrilateral element connected to the C0-type of Reddy's third-order shear deformation theory and cell-based smoothed strains is presented in this paper. Reddy's theory surely uses the advantages and desirable properties of third-order shear deformation theory. Moreover, FGP plates with advanced material properties are changed from the bottom to the top surface, respectively. Numerical results and comparisons with other reference solutions indicate the accuracy and efficiency of the current element in the analysis of FGP plates.

Nonlinear dynamic analysis of aircraft CFRP sandwich wings under explosive blast loading: Introducing SVM-DNN algorithm to predict dynamical information

The aircraft wings are a crucial component, particularly during mechanical shock excitation. Thus, for the first time, an inventive adaptable model to simulate the nonlinear dynamics of the wings under explosive blast loading at the moment of the collision is described in this article. It is crucial to increase the structure's stability because of explosive blast loading. The mentioned structure is made of two composite face sheets and a carbon fiber-reinforced polymer (CFRP). Functionally graded (FG) graphene origami (GOri)-enabled auxetic metallic metamaterial (GOEAM) is introduced to improve the stability of this kind of applicable structure, especially in air maneuvers. The analysis is conducted utilizing Reddy's third-order shear deformation of Reddy theory (TSDRT), incorporating Hamilton's principle and Von Kármán nonlinear geometric assumptions. The governing and boundary equations are accurately computed at the domain and boundary edges of the doubly curved structure. The coupled mesh-free radial point interpolation method (MRPIM) and Newton-Raphson method are applied for numerically simulating the current doubly curved structure by employing Newmark's temporal integration method with a constant-average acceleration approach. The present findings are cross-checked against the machine learning method and open-source results from the literature. Based on physical data, machine learning integrates supervised machine learning to predict the nonlinear vibration of the system. In this case, nonlinear transient bending properties are found using hybrid machine learning methods and solutions. The findings demonstrate the significance of GOEAM for nonlinear vibrations of the composite system. The current study's conclusions could be used as a benchmark and useful recommendations for future structural design techniques with enhanced features.

Individual Educational Program for Slow Learner

Slow learner is a condition where students have intellectual potential slightly below the average. Due to abilities below the average of children at their age, slow learner student’s ability in learning is slower than children at their age. With this condition, slow learner students need special education programs to optimize their potential so they can obtain learning outcomes as level as other student at their age group. This study discusses a design of individual education programs for slow learners students based on Reddy's theory, including providing motivation, giving individual attention, developing self-confidence, developing the habit of completing assignments well, and repeating the study by teacher or parent. If the programs can be done consistently by teachers and parents, the outcome will be effective in supporting the optimal learning for slow learners. This research based on literature review on books, journals, and articles from several databases such as Proquest, Google Scholar, and Pubmed from 2006 to 2021.

Nonlinear and chaotic vibrations of FG double curved sandwich shallow shells resting on visco-elastic nonlinear Hetenyi foundation under combined resonances

In this study, the nonlinear and chaotic instability of functionally graded (FG) double curved shallow sandwich shells resting on a viscoelastic Hetenyi foundation, under simultaneous effect of in-plane and transverse excitations is studied. Employing the third-order Reddy theory and von-Karman relations and the Hamilton principle, the partial differential equations of motion under movable SS boundary conditions are derived. Introducing the trigonometric Airy stress function and applying the Galerkin’s method, the equations are reduced to a set of nonlinear ODEs with time. Then, under forcing resonance conditions and using the perturbation method, the modulation equations at the stationary conditions are derived and solved numerically. Then stability of non-trivial solutions for the resonance amplitude corresponding to the presence of limit cycle oscillation is investigated. Then by extracting the characteristic resonance amplitude curves, the effect of various parameters, including: frequency detuning parameter, in-plane excitation amplitude, linear, shear and nonlinear stiffness and damping parameters of the foundation on nonlinear response are analyzed. Finally, by extracting two degrees of freedom system time response, bifurcation and chaotic characteristic curves of the problem, the conditions for occurrence the periodic, double periodic, multi-periodic and chaotic behaviors under the simultaneous effect of parametric and internal resonances are studied comprehensively.

HISTORY OF EMOTIONAL SUFFERING: FROM EMOTIONS TO NEEDS IN THE HISTORY OF EMOTIONS

ABSTRACTQuestions about the nature of emotions and the role of emotional expressions have been addressed frequently in the study of the history of emotions. However, the extent to which emotional suffering is present in the cultures and societies of the past is seldom queried. Our first goal is to identify criteria that historians of emotions can use to evaluate the emotional suffering of the people they study. We locate these criteria not in the theory of emotions, whether Norbert Elias's psychoanalytic theory or William M. Reddy's theory of emotives, but in the theory of basic, universal human needs proposed by Richard M. Ryan and Edward L. Deci. Although we agree with most contemporary historians of emotions that emotions themselves can be understood only within the context of a particular culture, we propose that additional inquiry into basic needs and their satisfaction could help historians of emotions cast more light on the inner lives of the members of the societies they investigate. Our second goal is to apply these insights to the case of acedia, a peculiar psychological state experienced by the Desert Fathers. We examine what acedia was for the Desert Fathers by analyzing Evagrius's writings. Our goal here is to capture what historians of emotions regularly do; that is, we aim to reconstruct how monks of the fourth century felt, expressed, and thought about emotions from within their own monastic culture. In addition, we analyze acedia from the perspective of the theory of needs. In this way, we hope to show how the theory of needs can help historians in their endeavors to understand the past.

Refined Model of Thermoelastoplastic Bending of Layered Plates with Regular Structure. ІІ. Model Problems

For axisymmetrically loaded annular plates rigidly fixed on one edge and statically loaded on the other edge and for rectangular elongated plates subjected to cylindrical bending, we propose a simplified version of the refined theory (model problems) for which the complexity of realization is comparable with the complexity of the Reissner and Reddy theories. Specific calculations are performed for the case of thermoelastoplastic bending of these plates for different levels of thermal action. It is shown that, for relatively thick plates, neither the classical theory, nor the traditional nonclassical Reissner and Reddy theories guarantee the possibility of getting reliable results in finding deflections even under the conditions of rough accuracy equal to 10%. It is shown that, under the conditions of bending of layered metal-composite plates carried out at elevated temperatures in the vicinity of their supporting edges, we observe the appearance of edge effects characterizing the phenomenon of shear of these structures in the transverse direction. The traditional theories characterized by the low orders of approximation of transverse shears do not enable one to detect these local effects, which explains their quite rough accuracy. It is shown that, for the adequate analysis of thermoelastoplastic bending of relatively thin and relatively thick plates for which the materials of the phases of their compositions are linearly elastic, it is sufficient to apply the Reddy theory.

The Refined Model of Viscoelastic-Plastic Deformation of Reinforced Cylindrical Shells

The paper formulates the initial-boundary-value problem of the viscoelastic-plastic bending behavior of cylindrical circular shells cross-reinforced along equidistant surfaces. The instant elastoplastic deformation of the shell composition components is described by the governing equations of the theory of plastic flow with isotropic hardening. The viscoelastic deformation of these materials is described by the defining relations of the Maxwell - Boltzmann model of body. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The used system of two-dimensional resolving equations and the corresponding initial and boundary conditions make it possible to determine displacements and stress-strain state (including residual one) in materials of the composition of flexible cylindrical shells with varying degrees of accuracy. In this case, the weak resistance of the considered composite structures to transverse shears is taken into account. In the first approximation, the equations are used, the initial and boundary conditions correspond to the relations of the widely used non-classical Reddy theory. A numerical solution of the initial-boundary-value problem posed is constructed using an explicit step-by-step "cross" scheme. The elastoplastic and viscoelastic-plastic dynamic deformation of a relatively thin long circular cylindrical shell is investigated. The structure is rationally reinforced in the circumferential direction and is loaded with an internal pressure of an explosive type. It has been demonstrated that under intense short-term loading even of a relatively thin cylindrical reinforced shell by internal pressure, the traditional Reddy theory does not guarantee that the maximum residual deflection and the intensity of residual deformations of the components of the composition are accurate to within 10% compared to calculations performed by the refined theory. The difference in the results of the corresponding calculations increases with an increase in the relative thickness of the composite shell. It was found that after plastic deformation of a long reinforced cylindrical shell in its residual state, not only appear zones of edge effects, but also a local zone of an intense deformation located in the vicinity of the central section of the shell. The length of the local central zone is comparable with the length of the zones of edge effects. It is shown that the amplitude of the transverse vibrations of the reinforced shell in the vicinity of the initial moment of time significantly (by an order of magnitude) exceeds the value of the maximum modulus of the residual deflection. Therefore, the calculations performed in the framework of the theory of elastoplastic deformation of composition materials do not allow a very approximate determination of the magnitude of the residual displacements and the magnitude of the residual deformed state of the components of the composition of the cylindrical shell.

Refined Model of Thermoelastoplastic Bending of Layered Plates with Regular Structures. I. Statement of the Problem

We formulate the problem of quasistatic thermoelastoplastic bending of layered plates with regular structures in the geometrically linear statement. The mechanical behavior of isotropic layers is described by the deformation-type relations of thermoelastoplasticity with regard for their different tensile and compression resistances. The linearized governing relations of layered media are deduced with the help of the method of variable parameters of elasticity. The obtained equations enable us to describe, with different degrees of accuracy, the stress-strain state of these plates by taking into account their weakened resistance to transverse shears. Note that the relations of traditional nonclassical Reissner and Reddy theories follow from these equations as particular cases. Within the framework of the proposed refined theories and Reddy theory, the force boundary conditions for tangential stresses are satisfied on the front surfaces. The boundary conditions for normal stresses are not satisfied on these surfaces. The variations of deflections across the thickness of the structures are not taken into account. The threedimensional equilibrium equations and the boundary conditions imposed on the end surface of the plate are reduced to two-dimensional relations by the method of weighted residuals. As weight functions, we use homogeneous polynomials in the transverse coordinate.

Buckling analysis of sandwich beam reinforced by GPLs using various shear deformation theories

In this research, the buckling analysis of sandwich beam with composite reinforced by graphene platelets (GPLs) in two face sheets is investigated. Three type various porosity patterns including uniform, symmetric and asymmetric are considered through the thickness direction of the core. Also, the top and bottom face sheets layers are considered composite reinforced by GPLs/CNTs based on Halpin-Tsai micromechanics model and extended mixture rule, respectively. Based on various shear deformation theories such as Euler-Bernoulli, Timoshenko and Reddy beam theories, the governing equations of equilibrium using minimum total potential energy are obtained. It is seen that the critical buckling load decreases with an increase in the porous coefficient, because the stiffness of sandwich beam reduces. Also, it is shown that the critical buckling load for asymmetric distribution is lower than the other cases. It can see that the effect of graphene platelets on the critical buckling load is higher than carbon nanotubes. Moreover, it is seen that the difference between carbon nanotubes and grapheneplatelets for Reddy and Euler-Bernoulli beam theories is most and least, respectively.

On the mathematical modeling of symmetric/asymmetric multi-layer orthotropic shells

In this paper, a mathematical model of multilayer orthotropic shells is developed on the basis of the third-order approximation of the Sheremetev–Pelekh–Reddy theory, taking into account geometric non-linearity. Conservative difference schemes of the considered model are derived and validated based on the variation-difference method. The influence of the number of layers on the stability of shells is considered. In addition, the stability of symmetric/asymmetric packages of multilayer shells is also discussed.

МОДЕЛИРОВАНИЕ УПРУГОВЯЗКОПЛАСТИЧЕСКОГО ПОВЕДЕНИЯ АРМИРОВАННЫХ ПЛАСТИН В РАМКАХ УТОЧНЕННОЙ ТЕОРИИ ИЗГИБА

The dynamic problem of elastic-viscoplastic deformation of flexible plates with spatial reinforcement structures is formulated. The plastic behavior of the components of the composition is described by equations of flow theory with isotropic hardening, taking into account the sensitivity of these materials to the rate of their deformation. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The relations used, with varying degrees of accuracy, describe the mechanical state of the bent plates and allow for the possible weakened resistance of the reinforced constructions to transverse shears. In a first approximation, the equations used, the boundary and initial conditions are reduced to the equalities of the widely used non-classical Reddy theory. To solve the stated nonlinear initial-boundary-value problem, a step-by-step algorithm is used, based on the use of an explicit numerical of the “cross” type scheme. The elastic-viscoplastic dynamic behavior of rectangular composite plates of different relative thicknesses under the action of a load corresponding to excess pressure in an air blast wave is investigated. Fiberglass-plastic and metal composite structures are considered. It is shown that for composite plates with a relative thickness of the order of 0.1, the calculation by the Reddy theory underestimates the maximum values of the strain intensity of the components of the composition by more than 12% compared with the calculation by the refined theory. A fairly simple Reddy theory is quite acceptable for calculating relatively thin plates. It is shown that for fiberglass-plastic plates with a relative thickness of the order of 0.1, replacing the traditional plane-cross reinforcement structure with the spatial structure of the reinforcement reduces the maximum deflection by more than 20%, and the greatest value of the strain intensity of the components of the composition is reduced by 10-20% or more. For metal-composite plates of any thickness and for fiberglass-plastic plates having a small relative thickness, the positive effect of from such a replacement of the reinforcement structures is practically not observed.

Моделирование вязкоупругопластического деформирования гибких пологих оболочек с пространственными структурами армирования

На базе процедуры шагов по времени построена математическая модель вязкоупругопластического поведения пологих оболочек с пространственными структурами армирования. Пластическое деформирование компонентов композиции описывается теорией течения с изотропным упрочнением; вязкоупругое деформирование - уравнениями модели Максвелла-Больцмана. Возможное ослабленное сопротивление композитных искривленных панелей поперечному сдвигу учитывается в рамках гипотез теории Редди, а геометрическая нелинейность задачи - в приближении Кармана. Решение сформулированной начально-краевой задачи строится с использованием явной численной схемы типа «крест». Исследовано упругопластическое и вязкоупругопластическое изгибное динамическое поведение «плоско»- и пространственно-армированных стеклопластиковых цилиндрических панелей под действием нагрузок взрывного типа. На примере относительно тонких композитных конструкций показано, что в зависимости от того, к какой лицевой поверхности (выпуклой или вогнутой) прикладывается нагрузка, замена традиционной «плоской» структуры армирования на пространственную может приводить как к увеличению, так и к уменьшению величины остаточного прогиба. Однако в обоих случаях такая замена позволяет существенно уменьшить интенсивность остаточных деформаций связующего материала и волокон некоторых семейств. Продемонстрировано, что амплитуды колебаний искривленных композитных панелей в окрестности начального момента времени значительно превосходят максимальные по модулю значения остаточных прогибов. При этом эпюры остаточных прогибов имеют достаточно сложный вид. Показано, что расчеты, проведенные в рамках теории упругопластического деформирования компонентов композиции, не позволяют даже приближенно определить величины остаточных деформаций материалов, составляющих композицию.

A refined model of viscoelastic-plastic deformation of flexible plates with spatial reinforcement structures

A refined model of viscoelastic-plastic deformation of flexible plates with spatial reinforcement structures has been developed. Strains of the composition materials are assumed to be small and decomposed into plastic and viscoelastic components. Instant plastic deformation of these materials is described by the flow theory with isotropic hardening. Viscoelastic deformation obeys the equations of a linear model of a five-constant body. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The possible weak resistance of composite plates to lateral shear is modeled in the framework of a refined theory of bending. This allows one to determine the displacements of plate points and the stress-strain state in the components of the composition with varying degrees of accuracy. In a first approximation, from the obtained equations and boundary conditions, we obtain relations corresponding to the traditional nonclassical Reddy theory. A numerical solution to the formulated initial-boundary-value problem is sought according to an explicit “cross-type” scheme The viscoelastic-plastic dynamic deformation of rectangular, relatively thin fiberglass plates under the influence of an explosive type load is investigated. The plates have a traditional plane-cross (orthogonal) or spatial reinforcement structure. It is shown that even in the case of relatively thin composite plates the Reddy theory is unacceptable for adequate calculations of their dynamic viscoelastic-plastic deformation. It has been demonstrated that the magnitude and shape of the residual deflections depend not only on the reinforcement structure, but also on the magnitude of the viscoelastic characteristics of the materials of the composition components. It was found that, after dynamic inelastic deformation, the composite plate can have a corrugated residual shape with folds oriented in the longitudinal direction. It is shown that even in the case of a relatively thin plate, replacing the planar-cross reinforcement structure with a spatial structure can significantly reduce the amount of residual deflection and the intensity of residual deformation in the binder material and some fiber families. For relatively thick plates, the effect of such a replacement of the reinforcing structures manifests itself much more.

Forced vibration analysis of concrete slabs reinforced by agglomerated SiO2 nanoparticles based on numerical methods

Abstract In this research, forced vibration analysis of a concrete slab reinforced by SiO2 nanoparticles is investigated. The Mori-Tanaka low is used for obtaining the material properties of nano-composite structure and considering agglomeration effects. By means of third order shear deformation theory or Reddy theory, the total potential energy of system is calculated. Also, using Hamilton’s principle, the coupled motion equations are obtained. Based on the harmonic differential quadrature method (HDQM), finite element method (FEM) and Newmark method, the frequency response of system is calculated. The effects of volume percent and agglomeration of SiO2 nanoparticles, boundary conditions and geometrical parameters of structure are shown on the frequency response of system. Results show that with growing the volume percent of SiO2 nanoparticles up to 0.37, the linear frequency of the structure is increased and the maximum dynamic deflection is decreased.

УТОЧНЕННАЯ МОДЕЛЬ ВЯЗКОУПРУГОПЛАСТИЧЕСКОГО ДЕФОРМИРОВАНИЯ ГИБКИХ АРМИРОВАННЫХ ПОЛОГИХ ОБОЛОЧЕК

The initial-boundary value problem of the visco-elastic-plastic behavior of flexible shallow shells reinforced along parallel surfaces is formulated. The inelastic behavior of the materials of the components of the composition is described by the equations of the theory of plastic flow with isotropic hardening. Viscoelastic deformation is determined by the relations of the Maxwell -Boltzmann model. Geometric nonlinearity is taken into account in the Karman approximation. The obtained resolving equations and boundary conditions allow with varying degrees of accuracy to determine the stress-strain state (including the residual state) in the components of the composition of curved panels. The low resistance of the reinforced structure to transverse shear is taken into account. In the first approximation, the equations and boundary conditions corresponding to the traditional non-classical Reddy theory follow from the relations obtained. The numerical solution of the formulated initial-boundary value problem is based on an explicit “cross” scheme. The features of visco-elastic-plastic dynamic deformation of an orthogonal reinforced cylindrical rectangular panel under the action of a load caused by an air blast wave are investigated. It is shown that in some cases even for relatively thin reinforced shallow shells, Reddy's theory is unacceptable for obtaining adequate results of calculations of their visco-elastic-plastic dynamic behavior. It has been demonstrated that the shape and size of the residual deflections of curved composite panels substantially depend on which face surface of the structure (convex or concave) an external load is applied. It was found that in both cases of loading, residual deflections lead to the formation of longitudinal folds in a thin cylindrical reinforced panel.

УТОЧНЕННАЯ МОДЕЛЬ ВЯЗКОУПРУГОПЛАСТИЧЕСКОГО ДЕФОРМИРОВАНИЯ ГИБКИХ АРМИРОВАННЫХ ПОЛОГИХ ОБОЛОЧЕК

The initial-boundary value problem of the visco-elastic-plastic behavior of flexible shallow shells reinforced along parallel surfaces is formulated. The inelastic behavior of the materials of the components of the composition is described by the equations of the theory of plastic flow with isotropic hardening. Viscoelastic deformation is determined by the relations of the Maxwell -Boltzmann model. Geometric nonlinearity is taken into account in the Karman approximation. The obtained resolving equations and boundary conditions allow with varying degrees of accuracy to determine the stress-strain state (including the residual state) in the components of the composition of curved panels. The low resistance of the reinforced structure to transverse shear is taken into account. In the first approximation, the equations and boundary conditions corresponding to the traditional non-classical Reddy theory follow from the relations obtained. The numerical solution of the formulated initial-boundary value problem is based on an explicit “cross” scheme. The features of visco-elastic-plastic dynamic deformation of an orthogonal reinforced cylindrical rectangular panel under the action of a load caused by an air blast wave are investigated. It is shown that in some cases even for relatively thin reinforced shallow shells, Reddy's theory is unacceptable for obtaining adequate results of calculations of their visco-elastic-plastic dynamic behavior. It has been demonstrated that the shape and size of the residual deflections of curved composite panels substantially depend on which face surface of the structure (convex or concave) an external load is applied. It was found that in both cases of loading, residual deflections lead to the formation of longitudinal folds in a thin cylindrical reinforced panel.

МОДЕЛИРОВАНИЕ ДИНАМИЧЕСКОГО ПОВЕДЕНИЯ ПРОСТРАНСТВЕННО-АРМИРОВАННЫХ ПЛАСТИН ИЗ НЕЛИНЕЙНО-УПРУГИХ МАТЕРИАЛОВ В РАМКАХ УТОЧНЕННОЙ ТЕОРИИ ИЗГИБА

Refined mathematical models are constructed for the flexible deformation of spatially reinforced flexible plates of nonlinear elastic materials of the composition components. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The obtained equations allow determining the deformed state of such structures with different degrees of accuracy taking into account their possible weak resistance to transverse shear. As a special case, based on these equations the relations of the traditional non-classical Reddy theory are obtained. The solution of the initial boundary value problem is obtained using an explicit numerical scheme of the “cross” type. It is shown that in a general case of plates an explicit numerical scheme cannot be developed for all spatial structures of reinforcement. The dynamic behavior is investigated for the flat and spatially reinforced plates of different shapes and relative thickness under the action of an air blast wave. It is shown that in the case of a strongly denominated anisotropy for relatively thick rectangular plates, the replacement of a flat structure with a spatial reinforcement structure reduces deflections modulo several tens of percent, and reduces the intensity of deformation of the components of the composition by several times. The reduction of the anisotropy degree of the composition and the relative thickness of the plates leads to a weakening of the effect of replacing the flat reinforcement structure on the spatial structure. This effect does not occur in annular plates with a rigid inner insert. On the contrary, the replacement of the flat reinforcement structure with the spatial structure leads to the deterioration of dynamic characteristics of such structures even of their relatively large thickness. It is shown that the dynamic behavior of plates calculated according to the Reddy theory significantly differ from the calculations according to the refined theory, especially when comparing the strain states of the components of the composition.

Buckling analysis of plates reinforced by Graphene platelet based on Halpin-Tsai and Reddy theories

In this paper, buckling analyses of composite plate reinforced by Graphen platelate (GPL) is studied. The Halphin- Tsai model is used for obtaining the effective material properties of nano composite plate. The nano composite plate is modeled by Third order shear deformation theory (TSDT). The elastic medium is simulated by Winkler model. Employing nonlinear strains-displacements, stress-strain, the energy equations of plate are obtained and using Hamilton's principal, the governing equations are derived. The governing equations are solved based on Navier method. The effect of GPL volume percent, geometrical parameters of plate and elastic foundation on the buckling load are investigated. Results showed that with increasing GPLs volume percent, the buckling load increases.

Vibration analysis of concrete foundation armed by silica nanoparticles based on numerical methods

In this study, vibration analysis of a concrete foundation-reinforced by SiO2 nanoparticles resting on soil bed is investigated. The soil medium is simulated with spring constants. Furthermore, the Mori-Tanaka low is used for obtaining the material properties of nano-composite structure and considering agglomeration effects. Using third order shear deformation theory or Reddy theory, the total potential energy of system is calculated and by means of the Hamilton\'s principle, the coupled motion equations are obtained. Also, based an analytical method, the frequency of system is calculated. The effects of volume percent and agglomeration of SiO2 nanoparticles, soil medium and geometrical parameters of structure are shown on the frequency of system. Results show that with increasing the volume percent of SiO2 nanoparticles, the frequency of structure is increased.

Optimisation of nanocomposite pipes under internal fluid reinforced by FRP and CNTs under seismic load

The optimisation approach can be applied to control the dynamic response of the mechanical problems. The design-based optimisation process can be provided the suitable performances of the complex engineering problem as nanocomposite pipes modelled by Reddy theory. In this work, a hybrid intelligent - analytical optimisation method is applied for maximising the critical velocity under frequency constraint. The adaptive dynamical harmony search (ADHS) is used in the optimisation process while a numerical approach is utilised in analytical process. In optimisation process basis ADHS, the memory is adjusted by a dynamic bandwidth while the best memory is adjusted by utilising normal random generated number. Four design variables are given in this problem as length to radius ratio, thickness to radius ratio, temperature and volume percent of carbon nano tube. The optimisation results for maximising critical velocity are compared for different fluid velocity at two levels of FRP layers of 1 and 2.