Vibration Analysis and Multi-Objective Optimization of Stiffened Triangular Plate (original) (raw)
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Multidisciplinary optimization of a stiffened shell by genetic algorithm
Journal of Mechanical Science and Technology, 2012
Vibration analysis of simply supported rotating cross-ply laminated stiffened cylindrical shell is performed using an energy approach which includes variational and averaging method. The stiffeners include rings and stringers. The equations are obtained by Rayleigh-Ritz method and Sander's relations. To validate the present method, the results are compared to the results available in other literatures. A good adoption is observed in different type of results including isotropic shells, rotating laminated shells, stiffened isotropic shells and stiffened laminated shells. Then, the optimization of parameters due to shell and stiffeners is conducted by genetic algorithm (GA) method under weight and frequency constraints. Stiffener shape, material properties and dimensions are also optimized.
Stiffened plates are used in many civil engineering, aerospace and marine structures. Adding stiffeners to a plate provides significant strength and stability while minor increase in weight to the structure. However, the mechanical behavior of stiffened plates is very complex. Numerous investigations were carried out in the past 50 years to examine the effects of stiffener/plate assembly geometries on buckling and collapse strength. Generally, there are two basic theories in literature for determining the optimal stiffener geometry of stiffened plates: the first one is based on the linear elastic or eigenvalue buckling theory, while the second one is centered around determining the ultimate strength or collapse load of the structure. In present paper, the critical stiffener geometries of longitudinally stiffened plates with flat stiffeners under uniaxial compression are investigated . Theoretical basis of the study is determining the ultimate strength of the plate considering plasticity and initial imperfections, which gives more rational and accurate result than the stiffener design methods based on the linear elastic buckling theory. Still, the principle of optimization is analogous. Both procedures consider optimal stiffener geometry as the point when further strengthening of the stiffeners becomes irrelevant to the buckling/ultimate strength in regards of the overall plate. Therefore, a series of nonlinear FEM analyses were carried out to determine the ultimate strength of various plate/stiffener assemblies. The numerical model was built in accordance with the Eurocode 3-1-5 standard, as well as the initial imperfection amplitudes and material properties. On the other hand, ultimate strength was computed with effective cross section method (ECSM) also as per EC3-1-5. Finally, results and comparison of the two methods (FEM and ECSM) are evaluated, conclusions about the possible optimal stiffener geometries are discussed.
Multi-objective optimization by genetic algorithm of structural systems subject to random vibrations
Structural and Multidisciplinary …, 2009
When attempting to optimize the design of engineered systems, the analyst is frequently faced with the demand of achieving several targets (e.g. low costs, high revenues, high reliability, low accident risks), some of which may very well be in con¯ict. At the same time, several requirements (e.g. maximum allowable weight, volume etc.) should also be satis®ed. This kind of problem is usually tackled by focusing the optimization on a single objective which may be a weighed combination of some of the targets of the design problem and imposing some constraints to satisfy the other targets and requirements. This approach, however, introduces a strong arbitrariness in the de®nition of the weights and constraints levels and a criticizable homogenization of physically different targets, usually all translated in monetary terms.
Use of genetic algorithms for the vibroacoustic optimization of plates
The Journal of the Acoustical Society of America, 1997
Optimal design of mechanical structures for vibration or noise reduction often requires finding the minima of highly nonlinear multi-dimensional functions. In this paper, genetic algorithms are introduced as a new promising tool for numerical optimization of such problems. The application presented is on the control of the vibroacoustic response of a plate carrying point-masses. Genetic algorithms have been used to determine the optimal positions of the masses on the plate. Several cases are presented, using various optimization criteria, showing the importance of selecting the most appropriate criterion.
Use of genetic algorithms for the vibroacoustic optimization of a plate carrying point-masses
Journal of the Acoustical Society of America, 1998
Optimal design of mechanical structures for vibration or noise reduction often requires finding the minima of highly nonlinear multi-dimensional functions. In this paper, genetic algorithms are introduced as a new promising tool for numerical optimization of such problems. The application presented is on the control of the vibroacoustic response of a plate carrying point-masses. Genetic algorithms have been used to determine the optimal positions of the masses on the plate. Several cases are presented, using various optimization criteria, showing the importance of selecting the most appropriate criterion.
Fundamental frequency optimization of variable stiffness composite skew plates
Acta Mechanica, 2020
In this study, natural frequencies and vibrational mode shapes of variable stiffness composite skewed plates are optimized applying a genetic algorithm. The variable stiffness behavior is obtained by altering the fiber angles continuously according to two selected curvilinear fıber path functions in the composite laminates. Fundamental frequency and related mode shapes of the plates are optimized for two different fiber path functions using the structural model obtained based on the virtual work principle. A three-layer composite skewed plate with four types of boundary conditions and different plate geometries is considered as case study in this research. Diverse sweptback angles as well as different aspect ratios are considered as various plate geometries. The present study aims to calculate the best fiber path with maximized fundamental frequency or in-plane strengths for a composite skewed plate. The generalized differential quadrature method of solution is employed to solve the governing equations of motion. Moreover, the linear kinematic strain assumptions are used, and the first-order shear deformation theory is employed to generalize the formulation for the case of moderately thick plates including transverse shear effects. Numerical results demonstrate the effect of the fiber angles, boundary conditions, and diverse geometries on the natural frequencies of the composite plate. The optimal fiber angles of each layer are presented for the above cases in free vibration analysis. It is verified that the application of optimized curvilinear fibers instead of the traditional straight fibers introduces a higher degree of flexibility, which can be used to adjust frequencies and mode shapes.
Discrete Optimization for Vibration Design of Composite Plates by Using Lamination Parameters
Advanced Composite Materials, 2009
A design method is proposed to optimize the stacking sequence of laminated composite plates for desired vibration characteristics. The objective functions are the natural frequencies of the laminated plates, and three types of optimization problems are studied where the fundamental frequency and the difference of two adjacent frequencies are maximized, and the difference between the target and actual frequencies is minimized. The design variables are a set of discrete values of fiber orientation angles with prescribed increment in the layers of the plates. The four lamination parameters are used to describe the bending property of a symmetrically laminated plate, and are optimized by a gradient method in the first stage. A new technique is introduced in the second stage to convert from the optimum four lamination parameters into the stacking sequence that is composed of the optimum fiber orientation angles of all the layers. Plates are divided into sub-domains composed of the small number of layers and designed sequentially from outer domains. For each domain, the optimum angles are determined by minimizing the errors between the optimum lamination parameters obtained in the first step and the parameters for all possible discrete stacking sequence designs. It is shown in numerical examples that this design method can provide with accurate optimum solutions for the stacking sequence of vibrating composite plates with various boundary conditions.
Vibration Optimization of Skew Composite Plates Using the Rayleigh-Ritz & Response Surface Methods
In this paper, the objective is to maximize the fundamental frequency of the laminated skew plates and the fiber orientation is considered as design variable. A pb-2 Rayleigh-Ritz method based on the first-order shear deformation theory (FSDT) is extended for the frequency analysis. The response surface method (RSM) is combined with the Rayleigh-Ritz method for optimal designs. The response surface of composite laminated structures is estimated using regression analysis in this study. Finally, the effect of skew angles, boundary conditions, aspect ratios and symmetric and anti-symmetric lay up on the optimal results is investigated and the results are compared with those available in literature.
GENETIC ALGORITHM ACTIVE VIBRATION CONTROL OF A FLEXIBLE PLATE STRUCTURES
Proceedings of the 51st Annual Meeting of the ISSS, 2007
This paper presents the development of an active vibration control (AVC) mechanism for a flexible plate structure using a Genetic Algorithm (GAs) strategy. The global optimisation technique of GAs is utilised to obtain a dynamic model of a flexible plate structure and verified within the AVC system. The GA based AVC algorithm thus developed is implemented within a flexible plate simulation environment and its performance in the reduction of vibration of the plate is assessed. The validation of the algorithm is presented in both the time and frequency domains. An assessment of the results thus obtained is given in comparison to the AVC system using conventional recursive least squares (RLS) method. Investigations reveal that the developed GA based AVC system performs better in the suppression of vibration of a flexible plate structure compared to an RLS based AVC system.