Multi-criteria optimal design of stiffened plates. Part 1. Choice of the formula for the buckling load (original) (raw)
Ultimate strength design of stiffened plates under axial compression and bending
Marine Structures, 1993
The basis for design of stiffened plates under longitudinal compression is outlined and predictions using several codes are compared against numerical results from an inelastic beam-column formulation and test results. In order to explore the inherent differences in column behaviour separately from discrepancies arising due to plate panel behaviour, the code predictions are re-evaluated adopting a common plate panel effective width formulation. On this basis, a critical review of code methods is made and some modifications are proposed. The effect of the magnitude and direction of applied uniform bending on the axial capacity of stiffened plates is investigated by comparing two alternative design approaches, namely an interaction equation and a method based on the Perry equation, against results from numerical analyses and from rigid plastic theory. The interaction equation is invariably more conservative than the Perry approach but its simplicity tends to be convenient for routine design applications. Finally, results of numerical analyses, together with experimental results from previous studies, on continuous stiffened plates under combined axial compression and lateral pressure are presented and available design guidance is discussed.
Applied and Computational Mechanics, 2020
Constructal design, finite element method and exhaustive search are applied to analyze different arrangements of steel plates with rectangular or trapezoidal stiffeners. As performance parameters, the maximum deflection and maximum von Mises stress are considered. A non-stiffened plate adopted as reference is studied together with 25 plates with rectangular stiffeners and 25 plates with trapezoidal stiffeners. The results show that trapezoidal stiffeners are more effective in minimizing the maximum deflection in comparison with rectangular stiffeners. However, regarding the minimization of stress, the rectangular stiffeners normally present better performance. When both performance parameters are concomitantly considered, a slight advantage of 4.70% for rectangular geometry is identified.
Optimization of an Orthogonally Stiffened Plate Considering Fatigue Constraints
Design, Fabrication and Economy of Welded Structures, 2008
The aim of this work is the optimization of a uniaxially compressed stiffened plate subjected to static and fatigue loading. The design variables are the thickness of the base plate, the number and stiffeners of the orthogonally stiffened plate. The constraints deal with the static overall plate buckling, the stiffener failure and the fatigue strength of the welded connections between the stiffeners and the interaction of the two types of failure. The cost function includes the cost of material, assembly, welding and painting. Randomness is considered both in loading and material properties. A level II reliability method (FORM) is employed. The overall structural reliability is obtained by using Ditlevsen method of conditional bounding. The costs of the plate designed to ensure a stipulated probability of failure will be compared with the solutions obtained for a code based method, which employs partial safety factors.
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.
The new simple design equations for the ultimate compressive strength of imperfect stiffened plates
Ocean Engineering, 2007
The new simple design equations for predicting the ultimate compressive strength of stiffened plates with initial imperfections in the form of welding-induced residual stresses and geometric deflections were developed in this study. A non-linear finite element method was used to investigate on 60 ANSYS elastic-plastic buckling analyses of a wide range of typical ship panel geometries. Reduction factors of the ultimate strength are produced from the results of 60 ANSYS inelastic finite element analyses. The proposed design equations have been developed based on these reduction factors. For the real ship structural stiffened plates, the most general loading case is a combination of longitudinal stress, transverse stress, shear stress and lateral pressure. The new simplified analytical method was generalized to deal with such combined load cases. The accuracy of the proposed equations was validated by the experimental results. Comparisons show that the adopted method has sufficient accuracy for practical applications in ship design.
Thin walled stiffened plates: optimization using lamination parameters
Brazilian Journal of Development
The leading guide, when it begins the design of aeronautical structures, is to reduce its weight to the minimum necessary. The use of composite materials in aeronautical structures has provided a considerable reduction in weight while maintaining the same structural strength. However, due to the anisotropy of the material, its mathematical model is complex and involves large matrices. In this work, a carbon fiber reinforced plate is optimized that withstands buckling compression loads and has its weight reduced to the minimum required. The Nastran optimizer will be employed whose objective function involves minimizing the weight of the structure to withstand a predefined load without buckling, and the thickness of the plate and stiffener are the design variables. Initially, the optimizer is used on an aluminum and carbon fiber plate, and its results are compared to validate the use of the optimizer. Then the optimizer is employed to obtain the optimum lamination parameters, thickness, and dimensions of the plate and stiffener. It´s necessary to have a lamination data to get the optimum lay-up.
A New Design Model for Ultimate and Buckling Strength Assessment of Stiffened Plates
2001
This paper presents a new computerized design model for the buckling strength assessment of stiffened panels. The overall formulation is very general, and in principle, any type of stiffening arrangements of open or closed profile type, corrugations, etc., can be analyzed. The model is based on an orthotropic version of Marguerre's non-linear plate theory. The stiffened panel is treated as an integrated unit, allowing for internal redistribution of membrane stresses between component plates while preventing overall buckling and permanent deformations/sets. The mode also provides a set of reduced anisotropic/orthotropic macro material coefficients that can be used in refined linear global finite element analysis of ship hulls in order to reflect the increased membrane flexibility experienced by compressed stiffened panels. This area of application allows for redistribution of loads between gross elements such as stiffened panels, frames, girders, bulkheads, and ensures a more rea...
Structural optimization strategies for simple and integrally stiffened plates and shells
Engineering Computations, 2005
Purpose – Shells are widely used structural systems in engineering practice. These structures have been used in the civil, automobile and aerospace industries. Many shells are designed using the finite element analysis through the conventional and costly trial and error scheme. As a more efficient alternative, optimization procedures can be used to design economic and safe structures. Design/methodology/approach – This
Welding in the World, 2006
Two types of stiffened plates are used in welded structures as follows: plates stiffened on one side and cellular ones, which consist of stiffeners welded between two deck plates. For a realistic cost comparison each type is optimized for minimum cost in the case of axial compression. Both plates are longitudinally stiffened by halved rolled I-section ribs. The deck plate thickness as well as the dimensions and number of stiffeners are sought, which minimize the cost function and fulfil the design and fabrication constraints. The cost function includes the material and fabrication costs. The design constraints relate to the overall and local plate buckling. It is shown that the cellular plate is cheaper than the plate stiffened on one side, since its large torsional stiffness enables us to use smaller plate thicknesses and smaller stiffener height.
Optimal Structural Design with Plate Finite Elements
Journal of the Structural Division, 1979
Yarious methods of optimization have been applied in the past few years to the minimum weight design of different structures such as trusses, frames, or built-up wings . Because the finite element method is general enough to handle any type of structure, finite element based optimization codes (1,17, have the added attraction of generality. However, while general purpose finite element programs, such as NASTRAN or SPAR (22) have a large repertory of finite elements, resizing capability in optimization codes has been mainiy Iimited to three types of finite elements: truss, membrane, and shear panels. These elements have in common the simplifying feature of a stiffness matrix that is linear in the resized dimension of the element. Other finite elements, such as beam or plate elements have a stiffness matrix that is a n<infinear function of resized dimensions. It is therefore more difficult to obtain the derivatives of the stiffness matrix with respect to design variables. However, because of the importance of beam and plate elements for finite element modeling the repertory of finite element based optimization codes must be expanded to include such elements. Plate bending elements are included in the DESAP I (8) structural optimization code, which uses the stress ratio lsshnique for stress constraints. Armand and Lodier pres€nt an optimality criterion for resizing plate elements limited to pure bending (2). The present work is concerned with the development of a general plate element (membrane + bending) resizing capability for a general purpose finite element based optimization code-Program for Analysis and Resizing of Structures (PARS) (5,16). Expressions for the derivatives of the stiffness matrixare presented and used to obtain derivatives of displacements and stresses. Note.-Discussion open until April I, 1980. To extend the closing date one month, a written request must be filed with the Editor of Technical Publications, ASCE. This paper is part of the copyrighted Journal of the Structural Division, Proceedings of the
Metals
Stiffened thin steel plates are structures widely employed in aeronautical, civil, naval, and offshore engineering. Considering a practical application where a transverse uniform load acts on a simply supported stiffened steel plate, an approach associating computational modeling, Constructal Design method, and Exhaustive Search technique was employed aiming to minimize the central deflections of these plates. To do so, a non-stiffened plate was adopted as reference from which all studied stiffened plate’s geometries were originated by the transformation of a certain amount of steel of its thickness into longitudinal and transverse stiffeners. Different values for the stiffeners volume fraction (φ) were analyzed, representing the ratio between the volume of the stiffeners’ material and the total volume of the reference plate. Besides, the number of longitudinal (Nls) and transverse (Nts) stiffeners and the aspect ratio of stiffeners shape (hs/ts, being hs and ts, respectively, the h...
Optimum design of plates structures under random loadings
Rem: Revista Escola de Minas, 2013
Structural optimization problems involving static loading have been studied for some time and in a way these kinds of problems are widely encountered in literature, but problems involving dynamic loading still have few studies not to mention problems involving nondeterministic dynamic loading. This paper presents a formulation of the optimization problem of plates subjected to random loadings. For the modeling of the structure, it used the bending plate element AST6 that explicitly provides these matrices, and dynamic mass reduction and rigidity matrices were used to reduce the computational cost of the problem. . The solution was achieved using the Interior Point Method and the sensitivity analysis of mass, and for the structure's stiffness matrixes the semi-analytical method was used. Three examples are presented to demonstrate the reliability of the process. The first example is an isotropic plate and the other two are problems involving sandwich plates. In all examples, an i...
Optimality criteria method for minimum weight design of plate structures
32nd Structures, Structural Dynamics, and Materials Conference, 1991
ber of active constraints in each cycle are limited to a small subset of the total constraints. Optimal design of plate struct,ures using This subset is updated in each cycle and the the Optimality Criteria Method (OCM) is dis-strategy allows the new constraints to enter cussed in this paper. The optimum designs while others leave. The OCM presented in are reached by just scaling the design vari-Ref. 1, consisted of two basic steps and they ables to an optimum intersection of multiple are referred to as resizing and scaling. Both constraints (compound scaling algorithm). A are iterative in the design space and their purfour-noded isoparametric plate element is used pose is to search for the optimum. The resizfor modelling the structure. Sensitivity com-ing algorithm is used when the design is on putations and the optimization algorithm are the constraint surface with respect t o one or discussed. The optimization cost involved (ex-more active constraints. It is derived directly cluding the finite element analyses) is minimal from the optimality conditions. The scaling compared to the mathematical optimization step on the other hand is t o bring the design algorithms. The procedure is demonstrated on t o the constraint surface when it is away from three example problems using stress and dis-the boundary. When the constraints and the placement constraints with side bounds on the objective are linear functions of the variables, design variables. the scaling to the constraint surface can be accomplished in a single step. Based on this * Associate Professor, Member AIAA nonlinear functions is the major advance in ** Graduate Research Assistant the application of OCM t o a wide variety of *** WL Fellow, Member AIAA mathematical optimization problems [6]. The
Optimization of Stiffened Plate Girders-An Overview
Generally Optimization aims to obtain the best results in a given circumstances or to minimize input to maximize the benefits. They are formulated to improve structural properties under consideration of specified constraints. The Optimization methods are nearly as old as calculus but reached prominence in the digital age. Nowadays numerous optimization techniques have been used in various fields. In this paper a basic overview of various research carried out on optimization of stiffened plate girders are discussed. Along with the optimization techniques, various experimental works on stiffened plate girders has also been discussed. Number of optimization techniques exists and it is not convenient to discuss about all those techniques. Considering that, an effort is made to concentrate on techniques that are commonly adopted for the past two decades.
Minimum cost design of a welded stiffened square plate loaded by biaxial compression
Structural and Multidisciplinary Optimization
The optimized plate structure consists of a simply supported square base plate stiffened with an orthogonal grid of flat stiffeners welded to the base plate by fillet welds. The uniformly distributed compressive load acts biaxially in the plane determined by the centre of gravity of T-sections, which consist of a part of the base plate and of a stiffener. In the optimization process the number of stiffeners as well as the thicknesses of the base plate and flat stiffeners, which minimize the cost function and fulfil the design constraints, as sought. The cost function includes the cost of material, assembly, welding and painting. Constraints relate to the global buckling, local buckling of base plate parts and stiffeners as well as to the deflection due to shrinkage of welds. To illustrate the effectiveness of the mathematical methods, the problem is solved by the Rosenbrock’s hill-climb algorithm as well as by entropy-based unconstrained minimization.
Two-Level Design Optimization for Compression Stiffened Panel
Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 2017
In this paper, a two-level design optimization approach is presented for compression stiffened panel sizing. First, the stiffened panel design procedure is described by means of a structural index concept. This method is based on the analytical formulations for structures and is used for the preliminary design level. In this procedure, the final results have a general form without being restricted by the geometrical parameters. The final results can be used for sizing different types of compression stiffened panels. Using the results obtained in the first level, the surrogate-based optimization is employed for design optimization in the second level. The analysis tool in the second level is the finite element method. Using Sequential Quadratic Programming algorithm, a novel technique is developed to find the global optimum of the surrogate model. The proposed two-level design approach is employed for design optimization of a flanged stiffened panel. In this panel design problem, which has six design variables, an initial training set with 57 points is created. Using 173 infill points, the optimum solution is obtained. In comparison with the conventional optimization methods, the surrogate modeling reduces the required nonlinear buckling analyses significantly. An estimate of the required number of analyses in the conventional methods is 57,201. The results of both levels are compared with each other. The final results of the optimization process are the optimum design non-dimensional ratios for plate elements of the flanged stiffened panel.
Vibration Analysis and Multi-Objective Optimization of Stiffened Triangular Plate
Volume 8: 26th Conference on Mechanical Vibration and Noise, 2014
In this paper, nonlinear vibration of a triangular shape plate, with several stiffeners, is studied. The governing equation of transversal deflection of the plate, with considering the effects of orthotropic characteristics and external excitation, is analyzed. The ordinary differential equation for the time response of the system, through employing the Galerkin method, is obtained; and the frequency response of the plateshape structure-using the multiple scale method-is determined. A robust genetic-based multi-objective optimization technique is employed to optimize the system's response by finding the optimum values of the geometry and locations of the plate's stiffeners. The influence of various parameters on the optimization results is investigated. According to the results, the optimum design of the stiffeners leads to a better performance of the vibration response.