Shape Of Stiffeners Research Articles

Design optimization of stiffening system for ocean thermal energy conversion (OTEC) cold water pipe (CWP)

Ocean thermal energy conversion (OTEC) uses heat from seawater to generate electrical energy by utilizing the temperature difference between the surface and deep ocean layer. Cold water pipe (CWP) attached to transport cold seawater over distances of up to 600 m to the plant is susceptible to failures caused by environmental loads. At this point, the CWP should be strengthened to prevent structural failure by inducing ring stiffeners along the pipe. To ensure its structural integrity, this study conducts a design optimization by investigating how the variation of ring stiffening system parameters such as height, thickness, distance between stiffeners, and shape of stiffeners influence the load-carrying capacity of the pipe using a Finite Element Analysis. Initially, the benchmarking procedure is done to ensure the reliability of the FEM modeling. After being verified, the modeling procedure is used for parametric study analyses. Results state that the higher and thicker stiffener ring increases the structural strength. In the case of the ring stiffener distance, as predicted, reducing the spacing between reinforcements is preferable to increasing the bending strength of CWP OTEC. Analyzing the variation of reinforcement height, thickness, and spacing, it was found that thickness had the most significant influence, followed by reinforcement height, and reinforcement spacing had the least. Additionally, changes in the shape of the reinforcement have minimal impact on the flexural strength of the structure when regions of identical moments of inertia exist.

Effects of stiffeners on anchor rod flexural strength in column base-plate connections

The present paper reports results of a numerical investigation of the mechanical behavior of a column base plate connection subjected to an axial compression force and a bending moment. A three-dimensional nonlinear model was developed, using the Cast3M software, and validated against experimental data. In addition, the material nonlinearity as well as contact conditions between the different components of the connection were thoughtfully considered. Based on the validated model, an extensive parametric analysis was conducted to investigate the effect of stiffeners on the forces in the anchor rods. The results clearly indicate that the design approaches that consider only the tensile strength of anchor rods while neglecting the bending moments can lead to a poor estimation of the forces applied to these rods. They also suggest that adding stiffeners provides additional strength and reduces the anchor rod bending in one direction. However, it is important to note that the stiffeners also induce an additional moment in the opposite direction. This could make the anchor rod more susceptible to biaxial bending with tension. Furthermore, this study proposes a new specific shape of stiffener is suggested (cbp5). It was concluded that the proposed shape of stiffeners allows a more uniform distribution of forces and avoids excessive stress concentrations, effectively prevents the biaxial bending in the anchor rod.

The efficiency of ring stiffener shape on the deformation of cylindrical shell structures – numerical analysis with solid finite element

The efficiency of ring stiffener shape on the deformation of cylindrical shell structures – numerical analysis with solid finite element

A review on buckling of the laminated composite panel under in-plane load

Abstract The review paper deals with a literature review on buckling analysis by different methods of laminated plates with different types of stiffeners which has been conducted in recent years. Analytical studies, experimental studies, finite element analysis, and other computational methods have been implemented by researchers on the stiffened panels under compression and shear for determination of the buckling behavior of the panel with I-type, blade-type, T-type, and hat-stiffeners. Some literature has been found on the panel with the influence of variation of the stiffener depth for the determination of buckling capacity. Very few literatures, non-linear finite element (FE) have been implemented for the determination of the effect of debonding damage between plate-stiffener of the panel but have not been reported parametric data about the effect of cohesive parameters of plate-stiffener and delamination of plies of the composites stiffened panel for post-buckling analysis. This paper also provides a literature survey based on the buckling performance of the plates with the application of different shapes of stiffeners.

Bio-inspired study of stiffener arrangement in composite stiffened panels using a Voronoi diagram as an indicator

Taking a biomimetic approach, this study introduces the use of a Voronoi diagram as an indicator of stiffener arrangement in stiffened composite panels. The locations of generator points that determine the shape of the Voronoi diagram are optimized for buckling problems under compression and shear load. An original optimization algorithm that combines the genetic algorithm and the finite element method is developed and implemented. The Voronoi diagram can also be used as an indicator for conventional, periodical stiffener shapes such as grid, lattice, honeycomb, and isogrid. We conducted parametric studies for periodical stiffener shapes, and demonstrated that these shapes can be designed using Voronoi diagrams. The results revealed that the optimized panel has a higher buckling load than that of conventional panels, and this methodology is effective for designing biomimetic stiffened CFRP panel structures.

Numerical Study of Ultrasonic Guided Wave in Composite Reinforced Panels with Different Stiffener Shapes

AbstractThe aim of this work is to propose a numerical methodology based on the finite element (FE) method to study the propagation mechanisms of transmitted, converted, and reflected guided waves in stiffened fiber‐reinforced polymeric (FRP) composite structures. The dispersion curves of such modes can help designers to improve the damage detection sensitivity of Lamb waves based structural health monitoring (SHM) systems. Using a FE model, whose accuracy is demonstrated against semi‐analytical data in a previous work, the phenomena of scattering and mode conversion in composite panels characterized by a structural discontinuity, such as a stiffener, are investigated. In particular, the behavior of guided waves is analyzed using stiffeners of different shapes, C and Omega shaped. The research activity makes it possible to highlight conversion of modes and reflected waves at stiffeners, providing new observations compared to the state of the art. The morphological complexities of the structure (thickness steps, multiple boundaries, stiffeners) can be used to redirect guided waves and to allow monitoring of a specific area. Wave reflections interacting with stiffeners, therefore, can be analyzed to improve diagnostics or design new detection strategies.

On the Optimal Shape and Placement of Longitudinal Stiffeners in Longitudinally Stiffened Plates

AbstractLongitudinal stiffeners are widely used in plated structures to prevent buckling of the slender plate elements and, therefore, to increase the load bearing capacity of these structures. There has been extensive research in the past regarding the shapes, sizes, and placement of these longitudinal stiffeners, however, there has been little research to make comparison between the different stiffener shapes across different numbers of stiffeners. The presented study compares the use of a single open stiffener, single closed stiffener, as well as the use of two open stiffeners. A numerical parametric study was conducted, considering different stiffener types, rigidities, and aspect ratios of the plates, for the cases of pure bending and compressions. The results of the study confirm that using a single closed stiffener or two open stiffeners is almost always more advantageous than the use of a single open stiffener. Furthermore, the study highlighted that it might be more advantageous to use two open stiffeners instead a single closed one.

Shape and Generalized Topology Optimization of Curved Grid Stiffeners Through the Level Set-Based Density Method

Abstract A shape and generalized topology optimization method based on the level set-based density method is proposed to design the curved grid stiffeners. The overall layout of the stiffeners is described by combining many single stiffeners, and each single stiffener is described by a level set function parameterized by using the compactly supported radial basis functions (CS-RBFs). The curvilinear path of each stiffener is described by the zero iso-contour of each level set function, and the width of each stiffener is described by applying an interval projection to each level set function. The combination operation that is similar to the Boolean operation “union” is achieved by using the p-norm method. The expansion coefficients of CS-RBFs are taken as part of the design variables of the optimization, and they are responsible for changing the shape of curved stiffeners. A topology design variable is assigned to each single stiffener, and it is responsible for changing the existence of single stiffeners. The proposed method is validated through several numerical examples, and the results demonstrate that the shape and topology of stiffeners can be effectively changed during the optimization.

Applications of bond-based cohesive peridynamics method (CPDM) to simulate inelastic fracture of stiffened plates in ship hull structures

In this work, we utilize a non-local bond-based cohesive peridynamics method (CPDM) that is recently developed in Han et al. (2022) to model and simulate crack growth and crack propagation in stiffened plates, and to predict inelastic fracture processes in extensively-used stiffened plates in ship hull structures.The bond-based cohesive peridynamics method has both normal and tangential components in the bond force density, which allow for capturing of inelastic fracture processes under large deformation, and it is capable of the description of complex nonlinear material constitutive behaviors.By doing so, we have systematically simulated the fracture of stiffened plates with different types of stiffeners, such as rectangular, I-shaped, and L-shaped. Moreover, we also studied the strength effects of different sizes, layouts, and shapes of stiffeners on the fracture of plates. In specific, we calculated the structure stress intensity factors for various stiffened plate structures and study the crack arrest effect for various types of stiffeners on the hull structures. The numerical results demonstrate that bond-based cohesive peridynamics provides an accurate and reliable modeling and simulation tool for studying the structural failure mechanism of ship hull structures and predicting crack growth in stiffened plates.

Structural Performance of Internally Stiffened Double-Skinned Profiled Composite Walls with Openings

The double-skin profiled composite wall (DSPCW) system, filled with concrete material, is favorable in modern structures due to its high strength and ductility. Openings may be required within this composite wall (DSPCW) for various reasons, similar to a conventional bearing wall, which can lead to a reduction in bearing capacity. Therefore, to avoid changes in the geometry, materials, and thickness of this DSPCW wall, a new internally stiffening concept has been suggested by providing embedded cold-formed steel tube (CFST) columns. For this purpose, two full-scale DSPCW specimens were tested under static axial load, one of which was fabricated with a large opening size and stiffened with two octagonal CFST columns, while the other was designed without an opening and served as a control wall specimen. The results showed that the stiffened DSPCW with an opening achieved a slightly lower ultimate bearing strength (−9.4%) than the control wall specimen, with no reduction in the ductility behavior. Furthermore, several finite element models of DSPCW have been analyzed and designed to investigate additional parameters that were not experimentally tested, including the effects of the embedded CFST column’s shape and different types of internal stiffeners longitudinally provided inside these columns. The numerical investigation confirmed that the embedded CFST column with an octagonal cross-section was more efficient compared to the hexagonal and rectangular shapes by about 11% and 18.4%, respectively. Furthermore, using internal steel stiffeners for embedded tubes with a T-shape improved the axial bearing capacity of the DSPCW with an opening slightly higher than the corresponding stiffened walls with other investigated stiffener shapes (V-shaped, U-shaped, and L-shaped).

A semi-analytical method for vibro-acoustic characteristics of orthogonal stiffened laminated cylindrical shells

This paper presents a semi-analytical model for vibro-acoustic characteristics of submerged orthogonal stiffened laminated cylindrical shells strengthened with orthogonal stiffeners. The first-order shear deformation theory (FSDT) combined with the Lekhnitsky smeared stiffener technique is adopted to describe the displacement field, and the spectral boundary element method is utilized to model the sound field. For modeling of a complex stiffened shell, the shell is divided into several main structures with the additional stiffness and mass of the smeared stiffeners. Then, the main structure is separated into sub-segments that match the boundary elements to ensure high accuracy of acoustic calculations. The continuous boundary conditions between sub-segments are simulated by using the artificial spring technique. The Fourier series and Legendre orthogonal polynomials are selected as admissible functions to describe the displacement field and the sound field. The vibration governing equations and Helmholtz integral equation are coupled with each other and solved simultaneously. High accuracy is demonstrated by comparing the results of the developed model with the literature. In numerical investigations, the influences of different external fluids, layup schemes, quantities and shapes of stiffeners (width and height) on vibro-acoustic characteristics of orthogonal stiffened laminated cylindrical shells (OSLCS) are investigated.

Numerical Investigation of the Flexural Performance of Slender CFST Beams with Varied Shapes of External Stiffeners

The concrete-filled steel tube (CFST) beams are recommended for adopting in the modern composite structure since it achieves a higher load capacity and ductility behaviour than the conventional structural members. Using CFST beams with slender steel cross-section led to reduce the overall cost of the structures compared to those with compact cross-sections; however, it is more likable to buckle under the compression stress. Therefore, providing external stiffeners along the four sides of CFST beams expected to reduce the overall self-weight also can provide more stiffening to the steel’s section that led to improve the loading capacity. In this study, a finite element (FE) method was adopted for numerically investigated the flexural performance of the square CFST beams stiffened with different shapes of external grooves that provided along the beam’s sides. The FE software named ABAQUS was adopted for this purpose where the original model of CFST beam analysed and verified with the corresponding tested specimen. After that, additional CFST model have been built and analysed to investigate further parameters including the effects of varied tube’s thickness, steel yielding strength, concrete compressive strength and different external grooves shape (V-shaped, U-shaped, C-shaped, double V-shaped). The results established from the numerical analyses showed that the ultimate bending capacity (Mu) of the stiffened CFST models was generally enhanced by increasing their concrete strength, steel yield strength and tube’s thickness but in varied percentages. For example, increasing the tube thickness from 1.5 mm to 3.0 mm achieved an improvement in Mu values of about 72.3\%. while fewer improvement percentages have been recorded of about 11.9\% when only the core concrete strength increased from 25 MPa to 55 MPa. Furthermore, the shape and number of grooves have positive impact on the bending capacity of stiffened CFST models, where using U-shape, C-shape and V-shape external grooves were led to improve the Mu value of about 2.8\%, 10.7\%, and 11.1\%, respectively. Thus, the energy absorption of these models was improved accordingly.

M-VCUT level set method for the layout and shape optimization of stiffeners in plate

Stiffened plates are widely used in engineering due to their relatively high rigidly-to-weight ratio. The stiffener layout and shape can significantly affect the mechanical properties of the plate. In this paper, a novel approach is developed in the framework of the Multiple Variable Cutting (M-VCUT) level set method for optimizing the layout and shape of stiffeners based on the Mindlin plate theory. In this approach, the layout and shape of stiffener can be controlled by adjusting the lower and upper limits of the design variables (cutting heights of the cutting surfaces at the cell nodes) conveniently. The coordinate mapping technique from the rectangular cell to the quadrilateral cell enables the shape of design domain to be arbitrary. In addition, multi-node cell with high-order polynomial interpolation technique is also applied for generating more complex geometry of stiffener. The numerical examples meshed by rectangular and quadrilateral cells are conducted for verifying the effectiveness of the proposed approach.

Stiffener layout optimization framework by isogeometric analysis-based stiffness spreading method

An innovative stiffener layout optimization framework is proposed based on the isogeometric analysis-based stiffness spreading method (IGA-based SSM), where the shape and size of stiffeners can be simultaneously optimized. The IGA-based SSM is employed to obtain the stiffness spreading matrices of the stiffeners that are embedded in the flat plate. The flat plate is modeled by high-order continuous isogeometric degenerated shell elements that can provide a smooth sensitivity field. Since the sensitivity required for the optimization can be obtained analytically, a gradient-based optimization algorithm can be employed. Moreover, the ground structure is used to provide the initial layouts of stiffeners and ensure the connectivity of stiffeners. A local geometry control strategy is also adopted to avoid the intersection of stiffeners in the optimization process. To verify the effectiveness and efficiency of the proposed method, typical illustrative examples are discussed in detail, considering the compliance minimization optimization problem. Compared with the continuum topology optimization method, the proposed method can provide a clear stiffener layout with a lower computational cost due to fewer design variables and fewer degrees of freedom of the optimization problem. Besides, the maximum thicknesses of stiffeners can be explicitly controlled, and it can easily solve the optimization problem of various volume fraction constraints. Finally, the proposed method is extended to solve a layout optimization problem of the engine nozzle adjusting plate under pressure loads, which obtains a good stiffener layout under the maximum displacement constraint.

Study on Optimal Design of a Folding-Type Hatch Cover Considering Material Selection

Most shipyard companies maintain efficiency in all aspects of their business to survive. One of these aspects is ship production costs and their reduction. This study proposes a solution to this problem using an optimization method. A hatch cover composed of plates and stiffeners was selected as a case study. In this study, the mass and material cost of the hatch cover was optimized as an objective function using the Pareto approach with developed optimization methods. Plate thickness t, stiffener shape s, and plate material type m were selected as the design variables in this study along with some constraints. To estimate the optimal plate thickness, an expression of stress equations was developed using an optimization technique. Furthermore, stiffener shape and plate material type selection were optimized using a genetic algorithm (GA). The results show that the optimization method is effective to decrease the mass and material cost of a hatch cover.

Simultaneous outline shape and size optimization for stiffeners in practical engineering structures

This article presents an engineering method to optimize the stiffener outline shape and cross-sectional sizes simultaneously for stiffened plate structures. A new optimization model for stiffened plate is established, and a hierarchical algorithm including external and internal optimization module is proposed to tackle the shape and size variables respectively. In external optimization, genetic algorithm (GA) is utilized to optimize binary-coded shape variables, and when calculating individual fitness values in GA, an internal optimization only involving size variables is carried out. For each individual, the stiffener outline shape is determined by a given shape variable vector and a reasonable finite element model could be automatically built with a parametric modeling method. The solution of internal optimization problem can be obtained by size optimization method, and an offset vector which updates during each cycle is created to modify the relative position of plate and stiffeners, ensuring the practicality of the optimal results in engineering. The presented approach is firstly verified through a typical example and then it is applied to the structural design of a micro-satellite. The results show that the method is effective in dealing with the simultaneous outline shape and size optimization problem of stiffeners, and the optimal results could be directly applied in practical engineering structures.

Optimal design of trapezoid stiffeners of composite cylindrical shells subjected to hydrostatic pressure

Optimization of a composite cylindrical pressure hull subjected to hydrostatic pressure with trapezoidal stiffeners is considered in this paper. The composite cylindrical shell is fabricated with carbon fiber reinforced epoxy composite while the stiffener is made of aluminum alloy. First of all, the analytical buckling model for composite cylinders with stiffeners subjected to hydrostatic pressure is derived. Subsequently, the finite element method is used to verify the accuracy of the analytical solution through some examples. After verification, the analytical solution is coupled with the genetic algorithm and then used to optimize the cross-sectional shape of the stiffeners of the composite pressure hull to obtain the maximum buckling pressure. During the optimization process, the relationship between the buckling pressure and each geometrical parameter of the stiffener has been analyzed. The inertia moment of the stiffener section is found to have a good linear relationship with the buckling pressure. Therefore, the inertia moment is used as an objective function to optimize the cross-sectional shape of the stiffeners of the composite pressure hull, and the feasibility of this method has been proved by comparing the optimization results. With high efficiency, this method can be applied to the optimal design of the stiffener shape of a composite pressure shell.

Finite Element Fatigue Analysis of Unsupported Crane

Abstract The presented strength and fatigue calculations refer to an unsupported deck crane and its three distinct parts: housing, jib and column. Static loads applied to the structure were due to the crane’s own weight and a maximum working load, corresponding to a maximum lifting capacity at a maximum outreach of the crane. The numerical analysis was aimed at determining the thickness of the skin plating of the column and the number, shape and distribution of stiffeners in the column, housing and jib, ensuring that the crane yields correct strength and fatigue parameters. During the process of designing marine structures, the standard numerical analysis is, in many cases, limited to calculations in the basic strength range. Even when using numerical methods of analysis, complex strength and fatigue calculations are often not performed. The modern numerical analysis chain for marine structures should concentrate not only on strength analysis, but should take a further step, which encompasses fatigue analysis. The article presents a new outlook on design methods, which should be the entry point to the design of marine structures. Based on the acquired number of cycles of fatigue life, it is possible to estimate, with a sufficient degree of accuracy, the practical service life of a structure. To solve the problem, the authors used the finite element analysis software ABAQUS supported by the fe-safe system.

Maximum buckling load of stiffened laminated composite panel by an improved hybrid PSO-GA optimization technique

A new strategy is proposed to find optimal fibers orientation of stiffened laminated composite panels to reach their maximum buckling load. To do so, buckling analysis of laminated stiffened composite panel is performed by using the ABAQUS software. A new hybrid algorithm based on the particle swarm optimization (PSO) and genetic algorithm (GA) is introduced for the optimization purpose. The conventional PSO method is improved by introducing a new inertia weight of velocity in the formulation. The validity of the proposed modeling technique is controlled by comparing the modeling results with that of experiment, and other previously published models and a satisfactory result has been achieved. Also, it has been found that the proposed optimization method has better performance than the existing methods, in terms of convergence speed and the accuracy of the algorithm. Moreover, the effects of shape of stiffeners, number of panel layers, curvature of panel, and boundary conditions on the optimal design are investigated.

Stability behaviour of stiffened curved plates subjected to pure compression

This paper investigates the stability behaviour and load carrying capacity of longitudinally stiffened, transversally curved steel plates under compressive stresses. The behaviour of stiffened, curved plates is a complex problem, especially due to the interaction of curvature, relative stiffness of the stiffeners and initial imperfections. A comprehensive parametric study is presented to investigate the effects of curvature, plate slenderness, size and shape of stiffeners on the ultimate resistance of stiffened curved plates. The aim of the study is to explain the behaviour of such structures and to demonstrate the benefits that can be obtained from bridge decks with curved plates. From the results some important conclusions are drawn regarding the structural behaviour and the positive effects of curvature on the cross-sectional resistance. A study on the influence of geometric imperfections on the load-bearing capacity is presented, which is based on the modification of nodal coordinates by means of sine-shape functions.