Optimizing Lamination of Hybrid Thick-Walled Cylindrical Shell under External Pressure by Using a Genetic Algorithm

Analysis of various thick-walled cross-ply composite cylindrical shells subjected to lateral pressures

The inverse problem of elastoplastic deformation of a thick-walled cylindrical shell of finite length under internal pressure is solved. For a given displacement of the outer surface of the shell, it was necessary to construct a numerical technique to determine the internal pressure providing this displacement. The problem being solved is a boundary value problem of a mixed type. The cylindrical shell under study is in a plane stress state and a volumetric deformed state. The mathematical formulation of the problem was based on the provisions of the deformation theory of plasticity. The strain state of the shell was described using nonlinear Hencky strains. The constructed model of elastic-plastic deformation of the shell took into account the compressibility of the material and the nonlinear law of hardening. The numerical calculation method is based on the method of variable elasticity parameters using the method of successive approximations, taking into account changes in the geometry of the shell during deformation. To assess the adequacy of the constructed numerical method for solving the inverse problem, a comparative calculation of the direct problem of elastoplastic deformation using the finite element method in the ANSYS 19.0 software package was carried out. The results obtained for radial and circumferential stresses, stress intensity, radial displacements of the boundary surfaces of a cylindrical shell at internal pressure calculated when solving the inverse elastoplastic problem showed sufficient consistency. The stress distribution patterns in the cylindrical shell wall according to the method of variable elasticity parameters and the finite element method are qualitatively the same. The differences in the quantitative results obtained according to the two approaches are no more than 10%. The proposed calculation method can be used in the field of aircraft engineering in order to calculate the required pressure when deforming cylindrical shells to the required geometry, taking into account the physical and geometric nonlinearities of the material under the condition of monotonic loading.

Pultruded glass fibre reinforced polymer (pGFRP) composites provide outstanding properties for composite polymer cross arms in power transmission line applications. This study has investigated the effects of various stacking sequences of fibres directions of pGFRP on flexural strength and creep behaviour. The use of static four-point bending flexural tests revealed that Stacking Sequence 2 (±45/0/90/0/90/0) had a significant flexural strength of 399.9 MPa while Stacking Sequence 1 (±45/90/0/±45) had a flexural strength of 242.5 MPa. Furthermore, the four-point bending creep experiments were performed at three distinct stress levels, notably 12%, 24%, and 37% of the ultimate flexural strength, to characterise the creep behaviour of distinct stacking sequences. Moreover, Findley’s power law equation for bending creep behaviour has revealed that the time-dependent reduction factor of Stacking Sequence 1 and Stacking Sequence 2 estimates a drop in flexural modulus of 23% and 10% respectively.

Effects of thermal residual stresses on failure of co-cured lap joints with steel and carbon fiber–epoxy composite adherends under static and fatigue tensile loads

Based on the Wilkins two-dimensional algorithm, a method is developed for the numerical study of the geometrically and physically nonlinear axially symmetrical dynamic stress-strain state of multilayer thick-walled cylindrical elastoplastic shells with different spiral reinforcement structures. A numerical study of the specific features in the nonlinear dynamic behavior of single-and two-layer cylinders is carried out for different reinforcement configurations and loading amplitudes.

This research discourse presents the development of a holistic mathematical model that is dedicated to showcase a set of analytical expressions for predicting global stiffness (axial stiffness, bending stiffness) and a material response characterization based on ply-per-ply in-plane stress investigations relevant to open-celled multidirectional curved cylindrical shell configurations. Additionally, the analytical model is shown to present the capability to mathematically determine the location of the centroid for thin-walled, composite cylindrical shells. The resulting centroidal expression for a composite system is essentially shown to be a primary function of material properties, composite stacking sequence, fiber orientation angle and the structural geometry as opposed to metal counterparts whose centroidal point is solely governed by their geometry. Analytical stress estimates are computed for thin-walled curved cylindrical shell constructions that are subjected to typical tension and longitudinal bending type loading conditions applied at the centroid under the presence and absence of a uniformly distributed thermal loading environment. A broad parametric investigation on the in-plane ply stresses (σx,σy,τxy) are conducted via choosing three fundamental parameters namely; varying mean radius of curvature, changing laminate thickness-to-mean radius ratio and increasing laminate thickness respectively. Three preferentially tailored variabilities in ply stacking sequence are established from a [(±45° / 0°]s symmetric-balanced composite lay-up to illustrate the effects on ply stresses. An ANSYS based finite element analysis scheme is employed to numerically determine the location of centroid and further substantiate the analytically acquired centroid predictions including and excluding the effects of temperature. The centroidal point is identified and its location is progressively reported for a fully open cross-sectioned curved strip to a fully closed cylindrical composite tube configuration by examining their distribution pattern as a function of circumferential arc angle (2α). FE tool is additionally utilized to compare the analytical stiffness predictions and analyze the validity of the in-plane analytical stress estimates. Excellent agreement is achieved in comparison between analytical solutions and computationally generated FE results. The central goal of this work is to demonstrate the potential of the formulated mathematical framework in accurately predicting the key mechanical attributes that dictates the structural behavior of curved composite shell members. This analytical model is designed to serve as a robustly efficient tool towards assisting structural design engineers in quickly gaining a broad fundamental understanding on the physical characteristics and structural response of such configurations by accurately conducting simple parametric studies during preliminary design phase prior to performing complex FE analyses.

The optimal stacking sequence and wall thickness of the composite strut tubes were determined to minimize thermal strains during orbital operation using generic algorithms and finite element analyses. From the results of previous thermal analyses of composite struts with various stacking sequences, the axial deformation is a matter of prime importance. For this reason, the optimization focuses to minimize the axial strains. The balanced and symmetric stacking sequences are used to minimize the radial and the twisting deformations. The genetic algorithm is known to be very effective for the discrete optimization such as stacking sequences of composite materials. As a result, the thermal deformations of the strut with an optimal stacking sequence are almost zero. The optimal strut tube consists of 6 plies and the weight of a composite strut is 22.4% that of aluminum strut. Finite element analyses showed that the optimal design of composite strut tubes withstood combined launch loads without buckling and failure. To validate the analyses, four composite struts were fabricated and their thermal strains were measured under the temperature increase of 100°C. The thermal and vibration experiments showed excellent correlations with analytical results.

Effects of stacking sequence and rotation angle of patch on low velocity impact performance of scarf repaired laminates

Stable axisymmetric vibrations of a thick-walled circular cylindrical shell made of a visco-elastic material are examined under pressure distributed in cylindrical surfaces which changes in time according to the law of harmonic. A system of four partial differential equations of the second order for defining the constituents of radial and axial displacements is written without any preliminary suppositions about the character of changes in unknown values on thickness. A spline-collocation method is used for decreasing the system dimension under an arbitrary way of fixing of sections. A corresponding boundary problem is numerically solved using a discrete Godunov method of orthogonalization.As an example the vibrations of shells with the same radius of the surface under various values of length and thickness. A comparison of results according to a strict and classic theory based on Kirchhoff−Love hypotheses is performed. Some peculiarities of changes on the radius of the radial displacement constituents which can not be detected in the frames of any approximated theory, assuming constancy of bending on the shell thickness are noted. Key words: axisymmetric vibrational bending, thick-walled cylindrical shell, visco-elastic material.

The artery is treated as a thick-walled cylindrical shell. Using the large deformation theory, an analytical expression for the pulse wave speed is obtained and the effect of twist on the wave speed is discussed. Numerical results indicate that although phase velocity increases with pressure, it decreases with increasing twist angle.

Composite beams, plates and shells are widely used in the aerospace industry because of their advantages over the commonly used isotropic structures especially when it comes to weight savings. Buckling analyses of composite structural components must be performed in order to ensure, for instance, that a composite panel designed to be part of a control surface does not buckle thereby compromising its aerodynamic shape. Optimization of composite structures has been performed in this paper using Genetic algorithm. Genetic algorithm (GA) approaches are successfully implemented for the TSP. The buckling load of composite plate, which is obtained by the Artificial Neural Networks, was used as the fitness function in the GA to find its optimized value by arranging the ply stacking sequence.

Deformation of laminated and sandwich cylindrical shell with covered or embedded piezoelectric layers under compression and electrical loading

In this study, the layer optimization was carried out for maximizing the lowest (first) fundamental frequency of symmetrically laminated square and rectangular laminated composite plates resting on rigid point supports distributed in eight different arrangements. Genetic Algorithm (GA) was used for searching the optimal stacking sequences of laminated composite plates, which is maximizing the first natural frequency defined as an objective function (fitness function). The first natural frequencies of the composite plates with various stacking sequences was calculated using the finite element method (FEM). However, the calculation of the first natural frequency for each new lay‐up sequence and point‐support arrangement needs a longer time than the evaluation period of GA. In order to reduce the searching time of the optimal lay‐up sequence, the artificial neural network models were proposed and trained with small training and testing data composed of the natural frequencies of the composite plates calculated for random lay‐up sequences, layer number, eight‐point support arrangements, and four‐plate length/width ratios using the FEM. The GA combined with these trained neural networks predicted successfully the optimal layer sequences without yielding a local optimum on the contrary the Ritz‐based layerwise optimization method (Narita and Hodgkinson, Compos. Struct., 69, 127 (2005)). The maximized fundamental frequencies were always better than those obtained for typical cross‐ply, angle‐ply, and quasi‐isotropic lay‐ups. Theeffects of the rigid‐point support locations, the optimum fiber orientation angles and the layer number on the maximum lowest natural frequency are also discussed. POLYM. COMPOS., 2011. © 2011 Society of Plastics Engineers

Rotating cylindrical shells serve as critical components in aerospace/mechanical engineering applications. However, certain faults inevitably occur during both manufacturing and operation, such as thickness non-uniformity caused by machining errors and bolt loosening during service. In our previous research, we systematically analyzed the mode localization phenomena induced by these two typical faults. The occurrence of mode localization significantly affects the dynamic characteristics of cylindrical shells, which may not only generate abnormal noise impacting the environment, but even endanger structural stability and safety. Therefore, it is of great significance to conduct active vibration control research on rotating cylindrical shells under these typical fault conditions. The force-electric coupling equation of the piezoelectric patches and the cylindrical shell was established. First, the Linear Quadratic Gaussian (LQG) control method was adopted for the active vibration control. In view of the characteristics of mode localization, the positional relationship between piezoelectric sensors and actuators and localized flexural deformation was considered, and the control effects of different arrangement methods were analyzed. On this basis, an accurate control method for piezoelectric vibration based on a genetic algorithm is proposed. The genetic algorithm is used to obtain the optimal input voltage for each piezoelectric actuator, which accurately suppresses localized flexural deformation without changing the overall flexural deformation.

1. Calculations for a three-layered cylindrical shell with R/h = 10 showed that for all the examined criteria of quality of the design the greatest effectiveness of the design is attained in the case of a “hybrid” stack whose inner and outer layers are reinforced circumferentially, the middle layer (h 2 * ≊ 0.4 h) is a dispersely reinforced composite. 2. In comparison with the best shell designs with plane reinforcement of the layers, such a “hybridization” of the stack makes it possible to increase the indicators of effectiveness additionally by 8.8 to 16.5% in dependence on the state of stress and strain of the shell. 3. The results of a comparison of the calculations carried out with four different kinematic shell models are in agreement with the conclusions of [7] as regards the possibility of using the simplest kinematic homogeneous models in engineering calculations of stability and vibrations; however, these models take transverse shear and compression of the normal of a thick-walled laminated structure into account.