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.

Effect of mold and core preheating temperature on corrosion resistance of casting Al-12Si alloy U-shaped cooling channel

Temperature has an important impact on the corrosion resistance of mold with cooling channels prepared by casting method.The effect of preheating temperature of the mold and the carbon fiber core on the roughness and corrosion resistance of U-shaped cooling channels made of Al-12Si alloy was examined in depth.The experimental results suggest that as the preheating temperature increased from 273 K to 573 K,the roughness of the inner wall of the cooling channel reduced from 96.6μm to 77.0μm.When the preheating temperature continued to increase to 723 K,the roughness increased to 85.3μm.The wetting between the Al melt and the carbon fiber will reduce micro bubbles and waves on the channel wall as the preheating temperature rises,thereby reducing the roughness.However,with the further increase of preheating temperature,it will increase the solidification time of the Al melt.At this time,the carbon fiber and Al melt will take more time to react,which increases the roughness of the channel wall to a certain extent.The results of exfoliation corrosion show that the larger roughness will aggravate exfoliation corrosion.The prolongation of high temperature reaction time between the carbon fiber and the Al melt will lead to the segregation of Si,which is easy to cause intergranular corrosion.Therefore,reasonable preheating temperature has an important impact on the roughness and corrosion resistance of U-shaped cooling channels.

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.

Lumbopelvic Fixation and Sacral Decompression for U-shaped Sacral Fractures： Surgical Management and Early Outcome

U-shaped sacral fractures are rare and often difficult to diagnose primarily due to the difficulty in obtaining adequate imaging and the severe associated injuries. These fractures are highly unstable and frequently cause neurological deficits. The majority of surgeons have limited experience in management of U-shaped sacral fractures. No standard treatment protocol for U-shaped sacral fractures has been available till now. This study aimed to examine the management of U-shaped sacral fractures and the early outcomes. Clinical data of 15 consecutive patients with U-shaped sacral fracture who were admitted to our trauma center between 2009 and 2014 were retrospectively analyzed. Demographics, fracture classification, mechanism of injury and operative treatment and deformity angle were assessed. All the patients were treated with lumbopelvic fixation or （and） sacral decompression. EQ-5d score was applied to evaluate the patients＇ quality of life. Of the 15 consecutive patients with U-shaped sacral fracture, the mean age was 28.8 years （range： 15-55 years） at the time of injury. There were 6 females and 9 males. The mean follow- up time was 22.7 months （range： 9-47 months） and mean full weight-bearing time was 9.9 weeks （range： 8-14 weeks）. Ten patients received lumbopelvic fixation and sacral decompression, one lombosacral fixation, and 4 merely sacral decompression due to delayed diagnosis or surgery. The post-operation deformity angle （mean 27.87°, and range： 8°-90°） of the sacrum was smaller than that pre-operation （mean 35.67; range： 15-90） with no significance difference noted. At the latest follow-up, all patients obtained neurological recovery with different extents. Visual analogue score （VAS） was reduced from preoperative 7.07 （range： 5-9） to postoperetive 1.93 （range： 1-3）. All patients could walk without any aid after treatment. Eight patients were able to care for themselves and undertook some daily activities. Five patients had returned to work full time. In conclusion, lumbopelvic fixation is an effective method for stabilization of U-shaped sacral fractures with fewer complications developed. Effective reduction and firm fixation are the prerequisite of early mobilization and neurological recovery. Sacral decompression effectively promotes neurological recovery even in patients with old U-shaped sacral fractures.

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.

GENERAL SOLUTION FOR U-SHAPED BELLOWS OVERALL-BENDING PROBLEMS

The formulae for stresses and angular displacements of U-shaped bellows overall bending in a meridian plane under pure bending moments are presented based on the general solution for slender ring shells proposed by Zhu Weiping, et al. and the solution for ring plates. The results evaluated in this paper are compared with those on EJMA (standards of the expansion joint manufacturers association) and of the experiment given by Li Tingxilz, et al.

Electrokinetic flow in the U-shaped micro-nanochannels

U-shaped micro-nanochannels can generate significant flow disturbance as well as locally amplified electric field, which gives itself potential to be microfluidic mixers, electrokinetic pumps,and even cell lysis process. Numerical simulation is utilized in this work to study the hidden characteristics of the U-shaped micro-nanochannel system, and the effects of key controlling parameters(the external voltage and pressure) on the device output metrics(current, maximum values of electric field, shear stress and flow velocity) were evaluated. A large portion of current flowing through the whole system goes through the nanochannels, rather than the middle part of the microchannel, with its value increasing linearly with the increase of voltage. Due to the local ion depletion near micro-nanofluidic junction, significantly enhanced electric field(as much as 15 fold at V=1 V and P_0=0) as well as strong shear stress(leading to electrokinetic flow) is generated.With increasing external pressure, both electric field and shear stress can be increased initially(due to shortening of depletion region length), but are suppressed eventually at higher pressure due to the destruction of ion depletion layer. Insights gained from this study could be useful for designing nonlinear electrokinetic pumps and other systems.

Mechanical property of U-Shaped 65Mn steel bumpers for seismic base isolation

This study proposes a novel U-shaped 65Mn steel bumper as the displacement restraining device for base-isolated structures with laminated elastomeric rubber bearings.A series of bumpers with different geometric parameters were designed and tested under monotonic and cyclic quasi-static loading protocols.The experimental results from a total of 232 specimens were analyzed to develop an analytical model to calculate the backbone curve and the maximum elastic restoring force for U-shaped 65Mn bumpers.Thus,the analytical equations to calculate the elastic,hardening,and unloading stiffness of U-shaped 65Mn bumpers,as well as their maximum elastic restoring force,are validated by using an additional ten groups of bumpers with varying radiuses.These analytical equations can accurately predict the mechanical parameters of U-shaped 65Mn steel bumpers for a design purpose.

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.

PROBLEMS OF U-SHAPED BELLOWS WITH NONLINEAR DEFORM TION OF LARGE AXISYMMETRICAL DEFLECTION(Ⅰ)—COUNTING NONLINEAR DEFORMATIONS OF RING SHELLS AND COMPRESSED ANGLE OF BELLOWS

This paper follows the work of [1,2]. There are some progress in dealing with moderately small rotations (the squares of rotation angles are the order of magnitude of strains) of middle surface normals of inside and outside ring shells and compressed angle of bellows. Calculation results agree with experiments well. To bellow design, the method given in this paper is of practical value and the discussion of the influence of compressed angle on characteristic relation is helpful.

ON PROBLEMS OF U-SHAPED BELLOWS WITH NONLINEAR DEFORMATION OF LARGE AXISYMMETRICAL DEFLECTION(Ⅱ)——COUNTING VARIATION OF THICKNESS DISTRIBUTION

On the basis of paper [1], assuming the logarithm of thickness at arbitrary point on a U-shaped bellows meridian is linear with the logarithm of distance between that point and axis of symmetry, perturbation solutions of the corresponding problems of large axisymmetrical deflection are given. The effects of thickness distribution variation, which result from technology factors, on stiffness of bellows are discussed.

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.

An ultra-low specific on-resistance trench LDMOS with a U-shaped gate and accumulation layer

An ultra-low specific on-resistance （Ron,sp） oxide trench-type silicon-on-insulator （SOI） lateral double-diffusion metal-oxide semiconductor （LDMOS） with an enhanced breakdown voltage （BV） is proposed and investigated by simulation. There are two key features in the proposed device： one is a U-shaped gate around the oxide trench, which extends from source to drain （UG LDMOS）; the other is an N pillar and P pillar located in the trench sidewall. In the on-state, electrons accumulate along the U-shaped gate, providing a continuous low resistance current path from source to drain. The Ron,sp is thus greatly reduced and almost independent of the drift region doping concentration. In the off-state, the N and P pillars not only enhance the electric field （E-field） strength of the trench oxide, but also improve the E-field distribution in the drift region, leading to a significant improvement in the BV. The BV of 662 V and Ron,sp of 12.4 mΩ.cm2 are achieved for the proposed UG LDMOS. The BV is increased by 88.6% and the Ron,sp is reduced by 96.4%, compared with those of the conventional trench LDMOS （CT LDMOS）, realizing the state-of-the-art trade-off between BV and Ron,sp.

pH-dependent Synthesis of Octa-nuclear Uranyl-oxalate Network Mediated by U-shaped Linkers

In this work,we report a novel octa-nuclear uranyl(U8)motif[(UO2)8O4(μ3-OH)2(μ2-OH)2]4+embedded in a uranyl-oxalate coordination polymer(compound 1)based on a U-shaped linker with extra-long xylylene chains for stabilizing the resulting high-nuclear motif through additional cross-linking connectivity.A comparison with dimeric and monomeric uranyl compounds obtained at different pH value from the same hydrothermal system reveals that,solution pH plays a vital role in formation of this octa-nuclear uranyl motif by promoting hydrolysis of uranyl source.Since high similarity of eight uranium centers in this nearly planar U8 motif here,overlapping and broadening of signals in fluorescence,infra-red(IR)and Raman spectra can be found.