Buckling Optimization of Curved Grid Stiffeners through the Level Set Based Density Method

Stiffened structures have great potential for improvingmechanical performance,and the study of their stability is of great interest.In this paper,the optimization of the critical buckling load factor for curved grid stiffeners is solved by using the level set based density method,where the shape and cross section(including thickness and width)of the stiffeners can be optimized simultaneously.The grid stiffeners are a combination ofmany single stiffenerswhich are projected by the corresponding level set functions.The thickness and width of each stiffener are designed to be independent variables in the projection applied to each level set function.Besides,the path of each single stiffener is described by the zero iso-contour of the level set function.All the single stiffeners are combined together by using the p-norm method to obtain the stiffener grid.The proposed method is validated by several numerical examples to optimize the critical buckling load factor.

Protective performance of shear stiffening gel-modified foam against ballistic impact:Experimental and numerical study

As one of the most widely used personal protective equipment(PPE),body armors play an important role in protecting the human body from the high-velocity impact of bullets or projectiles.The body torso and critical organs of the wear may suffer severe behind-armor blunt trauma(BABT)even though the impactor is stopped by the body armor.A type of novel composite material through incorporating shear stiffening gel(STG)into ethylene-vinyl acetate(EVA)foam is developed and used as buffer layers to reduce BABT.In this paper,the protective performance of body armors composed of fabric bulletproof layers and a buffer layer made of foam material is investigated both experimentally and numerically.The effectiveness of STG-modified EVA in damage relief is verified by ballistic tests.In parallel with the experimental study,numerical simulations are conducted by LS-DYNA®to investigate the dynamic response of each component and capture the key mechanical parameters,which are hardly obtained from field tests.To fully describe the material behavior under the transient impact,the selected constitutive models take the failure and strain rate effect into consideration.A good agreement between the experimental observations and numerical results is achieved to prove the validity of the modelling method.The tests and simulations show that the impact-induced deformation on the human body is significantly reduced by using STG-modified EVA as the buffering material.The improvement of protective performance is attributed to better dynamic properties and more outstanding energy absorption capability of the composite foam.

Analyzing the Form-Finding of a Large-Span Transversely Stiffened Suspended Cable System: A Method Considering Construction Processes

The precise control of the shape of transversely stiffened suspended cable systems is crucial. However, existing form-finding methods primarily rely on iterative calculations that treat loads as fixed known conditions. These methods are inefficient and fail to accurately control shape results. In this study, we propose a form-finding method that analyzes the load response of models under different sag and stress levels, taking into account the construction process. To analyze the system, a structural finite element model was established in ANSYS, and geometric nonlinear analysis was conducted using the Newton-Raphson method. The form-finding analysis results demonstrate that the proposed method achieves precise control of shape, with a maximum shape error ranging from 0.33% to 0.98%. Furthermore, the relationships between loads and tension forces are influenced by the deformed shape of the structures, exhibiting significant geometric nonlinear characteristics. Meanwhile, the load response analysis reveals that the stress level of the self-equilibrium state in the transversely stiffened suspended cable system is primarily governed by strength criteria, while shape is predominantly controlled by stiffness criteria. Importantly, by simulating the initial tensioning process as an initial condition, this method solves for a counterweight that satisfies the requirements and achieves a self-equilibrium state with the desired shape. The shape of the self-equilibrium state is precisely controlled by simulating the construction process. Overall, this work presents a new method for analyzing the form-finding process of large-span transversely stiffened suspended cable system, considering the construction process which was often overlooked in previous studies.

Nonlinear Bend Stiffener Analysis Using A Simple Formulation and Finite Element Method

Flexible marine risers are commonly used in deepwater floating systems. Bend stiffeners are designed to protect flexible risel against excessive bending at the connection with the hull. The structure is usually analyzed as a cantilever beam subjected to an inclined point load. As deflections are large and the bend stiffener material exhibits nonlinear stress-strain characteristics, geometric and material nonlinearities are important considerations. A new approach has been developed to solve this nonlinear problem. Its main advantage is its simplicity; in fact the present method can be easily implemented on a spreadsheet. Finite element analysis using ABAQUS is performed to validate the method. Solid elements are used for the bend stiffener and flexible pipe. To simulate the near inextensibility of flexible risers, a simple and original idea of using truss elements is proposed. Through a set of validation studies the present method is found to be in a good agreement with the finite element analysis. Further, parametric studies are performed by using both methods to identify the key parameters and phenomena that are most critical in design. The most important finding is that the common practice of neglecting the internal steel sleeve in the bend stiffener analysis is non-conservative and therefore needs to be reassessed.

Key Techniques and Applications of Adaptive Growth Method for Stiffener Layout Design of Plates and Shells

The application of the adaptive growth method is limited because several key techniques during the design process need manual intervention of designers. Key techniques of the method including the ground structure construction and seed selection are studied, so as to make it possible to improve the effectiveness and applicability of the adaptive growth method in stiffener layout design optimization of plates and shells. Three schemes of ground structures, which are comprised by different shell elements and beam elements, are proposed. It is found that the main stiffener layouts resulted from different ground structures are almost the same, but the ground structure comprised by 8-nodes shell elements and both 3-nodes and 2-nodes beam elements can result in clearest stiffener layout, and has good adaptability and low computational cost. An automatic seed selection approach is proposed, which is based on such selection rules that the seeds should be positioned on where the structural strain energy is great for the minimum compliance problem, and satisfy the dispersancy requirement. The adaptive growth method with the suggested key techniques is integrated into an ANSYS-based program, which provides a design tool for the stiffener layout design optimization of plates and shells. Typical design examples, including plate and shell structures to achieve minimum compliance and maximum bulking stability are illustrated. In addition, as a practical mechanical structural design example, the stiffener layout of an inlet structure for a large-scale electrostatic precipitator is also demonstrated. The design results show that the adaptive growth method integrated with the suggested key techniques can effectively and flexibly deal with stiffener layout design problem for plates and shells with complex geometrical shape and loading conditions to achieve various design objectives, thus it provides a new solution method for engineering structural topology design optimization.

Mechanical and thermal postbuckling of FGM thick circular cylindrical shells reinforced by FGM stiffener system using higher-order shear deformation theory

The postbuckling of the eccentrically stiffened circular cylindrical shells made of functionally graded materials （FGMs）, subjected to the axial compressive load and external uniform pressure and filled inside by the elastic foundations in the thermal environments, is investigated with an analytical method. The shells are reinforced by FGM stringers and rings. The thermal elements of the shells and stiffeners in the fundamental equations are considered. The equilibrium and nonlinear stability equations in terms of the displacement components for the stiffened shells are derived with the third-order shear deformation theory and Leckhniskii smeared stiffener technique. The closed-form expressions for determining the buckling load and postbuckling load-deflection curves are obtained with the Galerkin method. The effects of the stiffeners, the foundations, the material and dimensional parameters, and the pre-existent axial compressive and thermal load are considered.

THE LAYOUT OPTIMIZATION OF STIFFENERS FOR PLATE-SHELL STRUCTURES

The plate-shell structures with stiffeners are widely used in a broad range of engineering structures. This study presents the layout optimization of stiffeners. The minimum weight of stiffeners is taken as the objective function with the global stiffness constraint. In the layout optimization, the stiffeners should be placed at the locations with high strain energy/or stress. Conversely, elements of stiffeners with a small strain energy/or stress are considered to be used inefficiently and can be removed. Thus, to identify the element efficiency so that most inefficiently used elements of stiffeners can be removed, the element sensitivity of the strain energy of stiffeners is introduced, and a search criterion for locations of stiffeners is presented. The layout optimization approach is given for determining which elements of the stiffeners need to be kept or removed. In each iterative design, a high efficiency reanalysis approach is used to reduce the computational effort. The present approach is implemented for the layout optimization of stiffeners for a bunker loaded by the hydrostatic pressure. The numerical results show that the present approach is effective for dealing with layout optimization of stiffeners for plate-shell structures.

Buckling analysis of functionally graded material(FGM) sandwich truncated conical shells reinforced by FGM stiffeners filled inside by elastic foundations

An analytical solution for buckling of an eccentrically stiffened sandwich truncated conical shell is investigated. The shell consists of two functionally graded material （FGM） coating layers and a core layer which are metal or ceramic subjected to an axial compressive load and an external uniform pressure. Shells are reinforced by stringers and rings, in which the material properties of shells and stiffeners are graded in the thickness direction following a general sigmoid law distribution. Two models of coated shell-stiffener arrangements are investigated. The change of the spacing between stringers in the meridional direction is taken into account. A couple set of three-variable- coefficient partial differential equations in terms of displacement components are solved by the Galerkin method. A closed-form expression for determining the buckling load is obtained. The numerical examples are presented and compared with previous works.

Nonlinear stability of functionally graded material(FGM)sandwich cylindrical shells reinforced by FGM stiffeners in thermal environment

In this paper, Donnell＇s shell theory and smeared stiffeners technique are improved to analyze the postbuckling and buckling behaviors of circular cylindrical shells of stiffened thin functionally graded material （FGM） sandwich under an axial loading on elastic foundations, and the shells are considered in a thermal environment. The shells are stiffened by FGM rings and stringers. A general sigmoid law and a general power law are proposed. Thermal elements of the shells and reinforcement stiffeners are considered. Explicit expressions to find critical loads and postbuckling load-deflection curves are obtained by applying the Galerkin method and choosing the three-term approximate solution of deflection. Numerical results show various effects of temperature, elastic foundation, stiffeners, material and geometrical properties, and the ratio between face sheet thickness and total thickness on the nonlinear behavior of shells.

Effect of stiffeners on crashworthiness of square aluminium columns considering damage evolution

Combining the optimization and FEM technology,crashworthiness of aluminum extrusions was studied for an automobile safety plan.The effects of longitudinal stiffeners on the crushing of stiffened square columns were studied considering the damage evolution.The numerical analysis was carried out by ABAQUS software.Subsequently,the collapse behavior of aluminum extrusion damage was validated by comparing against solution published in literature.Finally,in order to find more efficient and lighter crush absorber and achieving minimum peak crushing force,response surface methodology(RSM) has been applied for optimizing the aluminum extrusion tube.

A NEW DISPLACEMENT-TYPE STABILITY EQUATION AND GENERAL STABILITY ANALYSIS OF LAMINATED COMPOSITE CIRCULAR CONICAL SHELLS WITH TRIANGULAR GRID STIFFENERS

In this paper, based on the theory of Donnell-type shallow shell, a new displacement-type stability equations is first developed for laminated composite circular conical shells with triangular grid stiffeners by using the variational calculus and generalized smeared-stiffener theory. The most general bending stretching couplings, the effect of eccentricity of stiffeners are considered. Then, for general stability of composite triangular grid stiffened conical shells without twist coupling terms, the approximate formulas are obtained for critical external pressure by using Galerkin's procedure. Numerical examples for a certain C/E composite conical shells with inside triangular grid stiffeners are calculated and the results are in good agreement with the experimental data. Finally, the influence of some parameters on critical external pressure is studied. The stability equations developed and the formulas for critical external pressure obtained in this paper should be very useful in the astronautical engineering design.

Influence of local stiffeners and cutout shapes on the vibration and stability characteristics of quasi-isotropic laminates under hygro-thermo-mechanical loadings

The perforated stiffened panel is generally found as a sub-component of sophisticated structures.The fundamental purpose of this panel is to withstand against buckling under complicated loading and environmental conditions.Hence,an accurate knowledge of critical buckling behaviour of stiffened panels is very much essential for a reliable and lightweight structural design.In this paper,the focus is on quasi-laminated panels with different cutout shapes of various sizes and their responses to hygrothermal environments under nonlinearly varying edge loads and is compared with the locally stiffened panels.Towards this,the modelling of the panel and stiffener is done by adopting nine-noded heterosis plate elements and three noded beam elements respectively.The stiffener formulation is suitably modified in order to take the torsional effect also into consideration along with the effect of shear deformation.Initially,the plate and the stiffener elements are treated separately,and then the displacement compatibility is maintained between them by using the transformation matrix.For a given loading and geometric discontinuity,the stress distribution within the perforated panel is highly non-uniform in nature and hence a dynamic approach has been used to calculate buckling loads by adopting two sets of boundary conditions,one set for pre-buckling stress analysis and the second set for buckling analysis.Four different quasi-isotropic stacking sequences are deliberated in this work by varying different ply-orientation in each scheme.The study also addresses the effect of various parameters such as nonlinear loads,hygro-thermal loads,cutout size and shapes,position of cutout,stiffener parameters,stacking sequences,thickness of plate and boundary conditions.

Bending tests and finite element analysis of lipped channels with complex edge stiffeners and web stiffeners

In order to study the bearing capacity and stability behavior of cold-formed steel flexural members with complicated sections,a total of 12 specimens divided into 6 groups were tested,including 3 groups of pure bending tests and non-pure bending tests each.There were three types of sections considered in this investigation,including channels with complex edge stiffeners(called B1-section),Σsection with complex edge stiffeners(called B2-section),and channels with complex edge stiffeners and V-type web stiffeners(called B3-section).Local buckling,distortional buckling and interaction buckling between them were observed in tests.The experimental results indicate that the bending strengths of B2-section specimens were the largest of these three types of specimens under the same conditions.It is found that the bending strength of B2-section specimens was increased by 6.47%for pure bending state and 8.12%for non-pure bending state,compared with that of B1-section specimens.Bending strength of B3-section specimens was almost the same with that of B1-section specimens under pure bending,but a little smaller than that of B1-section under non-pure bending state.It is also shown that B2-section specimens have better plastic deformation behavior than the other two sections.In addition,a non-linear finite element model was presented and verified against tests.The finite element analysis results agree well with experimental bending strength and failure modes.

Rapid Modeling and Finite Element Analysis of Missile Stiffener

Stiffener is the important missile structure to ensure the structural strength of the missile. In order to improve the design efficiency and the quality of the missile stiffener, the methods of missile stiffener rapid modeling and analysis are proposed. First, the problems of traditional manual modeling of the stiffener are analyzed. According to the problems and actual requirement of modeling, volume decomposition method is used to divide the stiffener into the upper section, the lower section and the web in order for feature analysis and parameter extraction. Then based on the parameters the basic unit decomposed above is created for Boolean operation to establish the stiffener. Finally, a rapid stiffener modeling and analysis program were developed based on UG Open API, the modeling and analysis result validates the feasibility of the method.

Dynamic behavior of outburst two-phase flow in a coal mine T-shaped roadway:The formation of impact airflow and its disaster-causing effect

The study of the dynamic disaster mechanism of coal and gas outburst two-phase flow is crucial for improving disaster reduction and rescue ability of coal mine outburst accidents.An outburst test in a T-shaped roadway was conducted using a self-developed large-scale outburst dynamic disaster test system.We investigated the release characteristics of main energy sources in coal seam,and obtained the dynamic characteristics of outburst two-phase flow in a roadway.Additionally,we established a formation model for outburst impact flow and a model for its flow in a bifurcated structure.The results indicate that the outburst process exhibits pulse characteristics,and the rapid destruction process of coal seam and the blocking state of gas flow are the main causes of the pulse phenomenon.The outburst energy is released in stages,and the elastic potential energy is released in the vertical direction before the horizontal direction.In a straight roadway,the impact force oscillates along the roadway.With an increase in the solid–gas ratio,the two-phase flow impact force gradually increases,and the disaster range extends from the middle of the roadway to the coal seam.In the area near the coal seam,the disaster caused by the two-phase flow impact is characterized by intermittent recovery.In a bifurcated roadway,the effect of impact airflow on impact dynamic disaster is much higher than that of two-phase flow,and the impact force tends to weaken with increasing solid-gas ratio.The impact force is asymmetrically distributed;it is higher on the left of the bifurcated roadway.With an increase in the solid-gas ratio,the static pressure rapidly decreases,and the bifurcated structure accelerates the attenuation of static pressure.Moreover,secondary acceleration is observed when the shock wave moves along the T-shaped roadway,indicating that the bifurcated structure increases the shock wave velocity.

Assessment of the stiffened panel performance in the OTEC seawater tank design:Parametric study and sensitivity analysis

Ocean thermal energy conversion(OTEC)is a process of generating electricity by exploiting the temperature difference between warm surface seawater and cold deep seawater.Due to the high static and dynamic pressures that are caused by seawater circulation,the stiffened panel that constitutes a seawater tank may undergo a reduction in ultimate strength.The current paper investigates the design of stiffening systems for OTEC seawater tanks by examining the effects of stiffening parameters such as stiffener sizes and span-over-bay ratio for the applied combined loadings of lateral and transverse pressure by fluid motion and axial compression due to global bending moment.The ultimate strength calculation was conducted by using the non-linear finite element method via the commercial software known as ABAQUS.The stress and deformation distribution due to pressure loads was computed in the first step and then brought to the second step,in which the axial compression was applied.The effects of pressure on the ultimate strength of the stiffener were investigated for representative stiffened panels,and the significance of the stiffener parameters was assessed by using the sensitivity analysis method.As a result,the ultimate strength was reduced by approximately 1.5%for the span-over-bay ratio of 3 and by 7%for the span-over-bay ratio of 6.

Explicit Topology Optimization Design of Stiffened Plate Structures Based on the Moving Morphable Component(MMC)Method

This paper proposes an explicit method for topology optimization of stiffened plate structures.The present work is devoted to simultaneously optimizing stiffeners’shape,size and layout by seeking the optimal geometry parameters of a series of moving morphable components(MMC).The stiffeners with straight skeletons and the stiffeners with curved skeletons are considered to enhance the modeling and optimization capability of the current approach.All the stiffeners are represented under the Lagrangian-description framework in a fully explicit way,and the adaptive ground structure method,as well as dynamically updated plate/shell elements,is used to obtain optimized designs with more accurate analysis results.Compared with existing works,the proposed approach provides an explicit description of the structure.Thus,a stiffened plate structure with clear stiffener distribution and smooth geometric boundary can be obtained.Several numerical examples provided,including straight and curved stiffeners,hierarchical stiffeners,and a stiffened plate with a cutout,validate the effectiveness and applicability of the proposed approach.

Reliability assessment for serviceability limit states of stiffened deep cement mixing column-supported embankments

The reliability and deterministic analyses of wood-cored stiffened deep cement mixing and deep cement mixing column-supported embankments(referred to as WSCSE and DCSE,respectively)considering serviceability limit state requirements are presented in this paper.Random field theory was used to simulate the spatial variability of soil
cement mixing(SCM)material in which the adaptive Kriging Monte Carlo simulation was adopted to estimate the failure probability of a column
supported embankment(CSE)system.A new method for stochastically generating random values of unconfined compressive strength(qu)and the ratio(Ru)between the undrained elastic modulus and qu of SCM material based on statistical correlation data is proposed.Reliability performance of CSEs concerning changes in the mean(μ),coefficient of variation(CoV),and vertical spatial correlation length(θv)of qu and Ru are presented and discussed.The obtained results indicate that WSCSE can provide a significantly higher reliability level and can tolerate more SCM material spatial variability than DCSE.Some performance of DCSE and WSCSE,which can be considered satisfactory in a deterministic framework,cannot guarantee an acceptable reliability level from a probabilistic viewpoint.This highlights the importance and necessity of employing reliability analyses for the design of CSEs.Moreover,consideration of only μ and CoV of qu seems to be sufficient for reliability analysis of WSCSE while for DCSE,uncertainties regarding the Ru(i.e.both μ and CoV)and θv of qu cannot be ignored.

水下爆炸载荷下舰船板架边界撕裂损伤相似准数研究

为研究舰船板架在水下爆炸冲击波载荷作用下的变形及破损,结合现有试验数据,采用仿真和数据拟合的方法,展开了均布载荷下板架边界撕裂损伤的相似准数研究。首先,结合理论和数据分析得出,板架边界撕裂时的初始响应速度与破坏模式密切相关,且可清晰描述板架的不同毁伤模式;进一步通过仿真得出断裂应变、板厚、长宽比是影响板架边界撕裂的重要参量;最后,基于量纲理论建立了用于判定板架边界撕裂毁伤的拟合函数,并根据战场舰船损伤实例验证了该函数的有效性。研究结果表明,基于初始响应速度和考虑断裂应变等参量的无量纲数构建板架边界撕裂毁伤判据的方法是可行的,为舰船板架的毁伤相似研究提供了参考。