Structural acoustic optimization in the design of a multi-ply composite cylindrical shell

A finite element/boundary element design tool is used to perform a structural acoustic optimization on an eight-ply graphite epoxy cylindrical shell. The shell is subject to two external monopole sources vibrating at a single frequency. The goal of the optimization is the minimization of the sum of the squared pressure amplitudes within the enclosed acoustic cavity. The ply angles serve as the design variables in optimization. The optimal design was obtained after 15 iterations with a 2 dB reduction in the average interior sound pressure level. The ply angle orientation shifted from an initially symmetric lay-up to an unsymmetric lay-up in the final design.

Reinforced concrete (RC) frames are extensively used in construction of buildings worldwide. The conventional design of these buildings typically relies on a "trial and error" method, starting with initial dimensioning followed by validation of the preliminary design. This approach makes it difficult to calculate potential cost savings in materials, while maintaining structural safety. In recent decades, the need for more efficient, safe and rational seismic design procedures has led to an increasing interest in structural optimisation of RC frames. However, due to the complex non-linear behaviour of RC frames, arriving at their optimum design under earthquake excitations is challenging. Even at serviceability limit state, concrete cracking can lead to significant stiffness changes and redistribution of inertial forces, phenomena that are normally expected after steel yielding. To mitigate these drawbacks, numerous combinations of section dimensions and reinforcement arrangements can be considered as design variables during a structural size optimisation process. However, this is seldom done for RC frames, as it requires seismic analyses with a high level of accuracy, which can be computationally expensive. Meanwhile, design optimisation has been identified as a feasible way to reduced embodied carbon emissions in construction, and therefore, a change of design paradigms is necessary. The article aims to critically review the major developments in recent seismic design optimisation studies on RC buildings, focusing on structural size optimisation, with the goal of identifying the main achievements and limitations. Different design objectives in current seismic design optimisation procedures are first summarised. The key steps in structural optimisation are then discussed, including design variables, design constraints, application of optimization methodologies, and evaluation of seismic performance. Finally, the research gaps in this field are identified, and suggestions are provided for future research directions. This article contributes towards the development of more efficient seismic design methods for RC structures, which in turn can lead to more sustainable construction.

Based on a systematic literature review, no design guidelines addressing practical issues related to steel circular hollow section (CHS) members under hydrostatic pressure have been documented thus far, except for the design recommendations proposed by the European standard EN 1993-1-6 concerning the strength and stability of shell structures. Considering that the existing codes are often outdated and subject to improvement, there is a growing demand for modern solutions that can accurately replicate the stability loss response of equipment subject to external pressure. The development of a more direct and simple method, augmented by reliable computational techniques, is advisable to avoid the numerous challenges associated with manual calculations. This approach will streamline the design process and mitigate the complexity of current practical or technical approaches. Thus, this research has formulated a method to predict design strength through the direct application of the critical elastic buckling stress, determined from Generalised Beam Theory (GBT) analyses, induced by hydrostatic pressure in custom-crafted equations, finely tuned for this specific objective. The authors present a formulation of GBT to analyze the elastic buckling behavior of CHS subject to both combined axial compression and external pressure. This work provides an extensive study of the behavior of circular cylindrical shells under external loading conditions. It first introduces the analyses of GBT and the theoretical and empirical formulas applicable to this objective. It then describes the steps involved in the development and validation of a numerical model that simulates the response of circular cylindrical shells under hydrostatic pressure, conducting an extensive parametric study using finite element analyses (FEAs). The results from available tests validate the finite element (FE) model. Upon achieving adequate agreement between the generated numerical and experimental results, new resistance reduction curves for cylindrical shell members are developed based on the results of the parametric study. Additionally, the study compares the existing provisions of EN 1993-1-6 for the design of cylindrical shells under hydrostatic pressure. Finally, a statistical approach is adopted to compare the responses of cylindrical shells calculated according to the EN 1993-1-6 code recommendations with those obtained through the newly proposed method.

The optimization of the large structure with the layout of stiffener is considered by a new calculation method in this study. Many number of stiffener are attached to large structures. Optimization of the large structures with design variables of plate thickness and shape of stiffener is performed. However, in order to obtain a better optimal solution, the optimization of the structure with design variable of number of stiffener and allocation of stiffener is required. But, the optimization of structure with design variable of the number of stiffener and allocation of stiffener is not performed. There are two problems. The first problem is the FEM model. FEM models need some nodes at allocation of stiffener as a characteristic of FEM. When number of stiffener and allocation of stiffener are changed by the process of the optimization of the structure, number of nodes and allocation of nodes of FEM model is also changed. Therefore, in order to ensure consistency of mesh, it is necessary to remake FEM model. In order to optimize structural, it is necessary to examine many propositions for design. However it is difficult to create and analyze the proposition for design of many numbers in restricted time. The second problem is the optimization method. When the number and allocate of stiffeners are changed, the stricture is modified and the number of design variables is changed. The optimization problem with changed number of design variables cannot be optimized by standard optimization methods. The methods of solving these problems are examined.

The composite cylindrical shell pressure structure is widely used for autonomous underwater vehicle (AUV). To analyze the critical buckling problem of variable stiffness (VS) composite pressure structure of AUV, a discrete finite element (DFE) method based on the curve fiber path function is developed in this work. A design and optimization method based on the radial basis function surrogate method is proposed to optimize the critical buckling pressure for a VS composite cylindrical shell. Both the DFE and surrogate methods are verified to be valid by comparison with the experimental data from the listed references. The effects of the geometric parameter and fiber angle on the critical buckling pressure are studied for different cylindrical shell cases. The results indicate that the proposed simulation model and optimization method are accurate and efficient for the buckling analysis and optimization of a VS composite cylindrical shell. Optimization result shows that the optimum critical buckling pressure for the VS cylindrical shell is improved and is 21.1% larger than that of the constant stiffness cylindrical shell under the same geometric and boundary condition.

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.

As the first part of an ongoing integrated project for developing a desktop gantry grinding machine tool, the structural optimization of column part is taken as the focus of the study.The thickness, height, and width of column are the design variables.The objective of optimization is to minimize volume while keeping the deformation of spindle tip smaller than the desired maximum value and the 2nd natural frequency below the given limit.Based on results of static and dynamic analyses obtained from finite element method, the response surface method with factorial design was utilized to create the metamodel for optimization.Two kinds of response surface model with two kinds of factorial design were used for comparison.The gradient search method was applied to the response surface model for optimization.The optimal structure of machine tool made the volume and the second natural frequency both decreasing 13% while the y-displacement of spindle tip were confined to required range.The result shows the successful application of response surface method with carefully chosen factorial design on structural optimization problem.

Free Vibrations of Composite Shallow Circular Cylindrical Shell Panels Stiffened by A Bonded Non-Central Shell Strip

Due to the high specific stiffness and strength, composite shells have been widely used in fuel tanks of launch vehicles. The buckling analysis of composite shells with cutouts based on the finite element (FE) method is too time-consuming. From the point-of-view of model size reduction, a novel Proper Orthogonal Decomposition (POD)-based buckling method is proposed in this paper, which can significantly increase the computational efficiency of buckling analysis. In order to improve the efficiency and effectiveness of prediction and optimization of composite shells with multiple cutouts, the POD method is integrated into an optimization framework that uses Gaussian process (GP) machine learning method. First, the training set used for the machine learning training is generated efficiently by means of the POD method. Then, the obtained set is trained and tested based on the Gaussian process method. The inputs are ply angles of the composite shell and the output is the buckling load of the composite shell containing cutouts. In order to maximize the buckling load of the composite shell against cutouts, the Genetic Algorithm is combined with the trained Gaussian process method to search for the optimal ply angles. Finally, an illustrative example is carried out to demonstrate the effectiveness of the proposed prediction and optimization framework.

This paper aims to obtain the optimal composite box-beam design for a helicopter rotor blade. The cross-sectional dimensions and the ply angles of the box beam are considered as design variables. The objective is to optimize the box beam to attain a target vector of stiffness values and maximum elastic coupling. The target vector is the optimal stiffness values of helicopter rotor blade obtained from a previous aeroelastic optimization study. The elastic couplings introduced by the box beam have beneficial effects on the aeroelastic stability of helicopter. The optimization problem is addressed by decomposing the optimization into two levels, a global level and a local level. The box-beam cross-sectional dimensions are optimized at the global level. The local-level optimization is a subproblem which finds optimal ply angles for each cross-sectional dimension considered in the global level. Real-coded genetic algorithm (RCGA) is used as the optimization tool in both the levels of optimization. Hybrid operators are developed for the RCGA, thereby enhancing the efficiency of the algorithm. Min–max method is used to scalarize the multiobjective functions used in this study. Optimal geometry and ply angles are obtained for composite box-beam designs with ply angle discretization of \(10\), \(15\), and \(45^o\).

The effects of thermal residual stresses, strains, and stacking sequences resulting from hybrid composite material system selection on the design of thick-walled cross-ply cylindrical shells are discussed by using a simple and accurate finite cylindrical element method formulated by Byon and Vinson [1]. It is seen that beneficial effects can be realized in the cylindrical shells by utilizing a hybrid of graphite/epoxy and E-glass/epoxy material systems. An optimal stacking sequence of hybrid composite cylindrical shell is also proposed to give the smallest value of tensile strain in the through-the-thickness direction. This paper describes an optimal stacking sequence of a thick-walled cross-ply cylindrical shell laminated with hybrid composite materials determined by a genetic algorithm (GA) and shows that this method is useful for such an optimization problem.

Investigation of Optimum Ply Angle using Finite Element (FE) Approach: References for Technical Application on the Composite Navigational Buoys

Fibre Reinforced Plastics (FRPs) have been used in many practical structural applications due to their excellent strength and weight characteristics as well as the ability for their properties to be tailored to the requirements of a given application. Thus, designing with FRPs can be extremely challenging, particularly when the number of design variables contained in the design space is large. For example, to determine the ply orientations and the material properties optimally is typically difficult without a considered approach. Optimization of composite structures with respect to the ply angles is necessary to realize the full potential of fibre-reinforced materials. Evaluating the fitness of each candidate in the design space, and selecting the most efficient can be very time consuming and costly. Structures composed of composite materials often contain components which may be modelled as rectangular plates or cylindrical shells, for example. Modelling of components such as plates can be useful as it is a means of simplifying elements of structures, and this can save time and thus cost. Variations in manufacturing processes and user environment may affect the quality and performance of a product. It is usually beneficial to account for such variances or tolerances in the design process, and in fact, sometimes it may be crucial, particularly when the effect is of consequence. The work conducted within this project focused on methodologies for optimally designing fibre-reinforced laminated composite structures with the effects of manufacturing tolerances included. For this study it is assumed that the probability of any tolerance value occurring within the tolerance band, compared with any other, is equal, and thus the techniques are aimed at designing for the worst-case scenario. This thesis thus discusses four new procedures for the optimization of composite structures with the effects of manufacturing uncertainties included.

Advanced Grid Stiffened(AGS) composite cylindrical shells are widely used in aerospace industry. This study analyzes the buckling loads for various types of grid structures of AGS composite cylindrical shells. The grid structures are classified as Angle-grid, Iso-grid, Kagome-grid, Ortho-grid, Orthotropic-grid and the characteristics had been analyzed for each grid type. In this study, the various types of grid structure were designed that weight of the whole structure keeps a constant. Under the condition of constant-weight, design variables such as grid angle, number of the grid, h/t ratio of the grid were controlled, and buckling loads of the grid structures were analyzed. The results were analyzed for each type of grid and each design variable of the structures. This study was performed through finite element method and the accuracy of the analysis was verified by previous studies. Finally, buckling modes were analyzed with the thickness of the skin. The selection for the most appropriate design variables had been verified for each grid type and the result can be applied to the optimization of grid structure design, and is also very helpful for reducing the computational cost and obtaining optimization values more accurately.

An automatic optimization approach for the structural design of turbine blade shroud is presented and applied to the optimal design of a zigzag shroud in this paper. It integrates commercial CAD and CAE softwares into optimization procedure iSIGHT. According to the normal rules of the shroud design and experience, this paper advises a zigzag shroud which is fit for a kind of turbine blade. The parametric model of the shroud is established and the pre-twist angle parameter is taken into consideration. The structural intensity performance of the shroud, which is used to compute the optimal objective and constraints during optimization, is determined by conducting coupled thermal-structural analysis of shrouded turbine blade using the commercial Finite Element code ANSYS. Two application examples of the optimization approach are presented, with optimal objective functions of shrouded blade mass and maximum shroud contact pressure respectively. The latter includes the pre-twist angle as one of design variables. Mechanical and geometry constraints are applied on the design to ensure that the optimized design meets requirements for feasibility of engineering criteria. Simulation results from shroud optimizations by means of the optimization approach prove that the performance of the shroud can be improved significantly through structure optimization. The optimization approach provides an effective method to design and optimize the similar complicated models.