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.

Plate/shell structure topology optimization of orthotropic material for buckling problem based on independent continuous topological variables

The purpose of the present work is to study the buckling problem with plate/shell topology optimization of orthotropic material. A model of buckling topology optimization is established based on the independent, continuous, and mapping method, which considers structural mass as objective and buckling critical loads as constraints. Firstly, composite exponential function (CEF) and power function (PF) as filter functions are introduced to recognize the element mass, the element stiffness matrix, and the element geometric stiffness matrix. The filter functions of the orthotropic material stiffness are deduced. Then these filter functions are put into buckling topology optimization of a differential equation to analyze the design sensitivity. Furthermore, the buckling constraints are approximately expressed as explicit functions with respect to the design variables based on the first-order Taylor expansion. The objective function is standardized based on the second-order Taylor expansion. Therefore, the optimization model is translated into a quadratic program. Finally, the dual sequence quadratic programming (DSQP) algorithm and the global convergence method of moving asymptotes algorithm with two different filter functions (CEF and PF) are applied to solve the optimal model. Three numerical results show that DSQP&CEF has the best performance in the view of structural mass and discretion.

Hydroelastic Analysis of Very Large Floating Structures Using Plate Green Functions

Great attention has been paid to the development of very large floating structures. Owing to their extreme large size and great flexibility, the coupling between the structural deformation and fluid motion is significant. This is a typical problem of hydroelasticity. Efficient and accurate estimation of the hydroelastic response of very large floating structures in waves is very important for design. In this paper, the plate Green function and fluid Green function are combined to analyze the hydroelastic response of very large floating structures. The plate Green function here is a new one proposed by the authors and it satisfies all boundary conditions for free-free rectangular plates on elastic foundations. The results are compared with some experimental data. It is shown that the method proposed in this paper is efficient and accurate. Finally, various factors affecting the hydroelastic response of very large floating structures are also studied.

Tectonic evolution of structures in Southern Sindh Monocline,Indus Basin,Pakistan formed in multi-extensional tectonic episodes of Indian Plate

There are a number of structures and structural styles found in extensional tectonic settings of the world,and it is a big challenge to study the evolution of these structures. Evolution of structures formed in extensional tectonic settings have been studied by researchers on different extensional basins of the world. Southern Sindh Monocline lies on the western corner of Indian Plate and the tectonic history of Indian plate has also experienced different extensional episodes, and its journey rifted from Gondwanaland to its final welding to Asia. The aim of this study is to figure out the evolution of structures in the subsurface of Southern Sindh Monocline, Pakistan using the seismic data interpretation and flattening of horizons approach. Structures within the subsurface of Southern Sindh Monocline have been characterized by different tectonic episodes of Indian plate while rifting from Gondwanaland, rifting from other plates at different geological times and to its collision with the Asia. Basic structures within study area are classified into nine types while the structural styles have been classified into six types as horst and grabens, dominos, crotch, synthetic and antithetic, negative and flashlight structural style. The structures within the study area revealed evidence for three major structural episodes which can be characterized as Episode 1: Structures associated with rifting of Indian plate from Gondwanaland during Late Jurassic to Early Cretaceous, Episode 2: Modification and reactivation of previous structures while Madagascar rifted from Indian Plate during the Middle Cretaceous and during Episode 3: Inversion and reactivation of structures occurred when Indian Plate collided with Asia during Early Eocene.

Power Flow Response Based Dynamic Topology Optimization of Bi-material Plate Structures

Work on dynamic topology optimization of engineering structures for vibration suppression has mainly addressed the maximization of eigenfrequencies and gaps between consecutive eigenfrequencies of free vibration, minimization of the dynamic compliance subject to forced vibration, and minimization of the structural frequency response. A dynamic topology optimization method of bi-material plate structures is presented based on power flow analysis. Topology optimization problems formulated directly with the design objective of minimizing the power flow response are dealt with. In comparison to the displacement or velocity response, the power flow response takes not only the amplitude of force and velocity into account, but also the phase relationship of the two vector quantities. The complex expression of power flow response is derived based on time-harmonic external mechanical loading and Rayleigh damping. The mathematical formulation of topology optimization is established based on power flow response and bi-material solid isotropic material with penalization(SIMP) model. Computational optimization procedure is developed by using adjoint design sensitivity analysis and the method of moving asymptotes(MMA). Several numerical examples are presented for bi-material plate structures with different loading frequencies, which verify the feasibility and effectiveness of this method. Additionally, optimum results between topological design of minimum power flow response and minimum dynamic compliance are compared, showing that the present method has strong adaptability for structural dynamic topology optimization problems. The proposed research provides a more accurate and effective approach for dynamic topology optimization of vibrating structures.

A new design of 3D-printed orthopedic bone plates with auxeticstructures to mitigate stress shielding and improve intra-operative bending

Orthopedic bone plates are most commonly used for bone fracture fixation for more than 100 years.The bone plate design had evolved over time overcoming many challenges such as insufficient strength and excessive plate–bone contact affecting the blood circulation.However,it is only made of two materials,either stainless steel(AISI 316L)or titanium(Ti–6Al–4V).There are two main limitations of metallic bone implants,namely stress shielding and the problem of malocclusion caused by the displacement of the fracture site during healing.To overcome the two problems,a new bone plate design with the incorporation of auxetic structures is proposed in this work.This study aims to use auxetic structure section in the bone plate that would decrease the stiffness of the region,thereby mitigating the stress-shielding effect and at the same time act as a deformable section to enable intra-operative bending for effective alignment while having enough bending strength and stiffness.Two different auxetic structures namely re-entrant honeycomb and missing rib structures were considered.The auxetic structure incorporated bone plates were designed,finite element analysis was done,fabricated using direct metal laser sintering technique,and tested.The results indicate that the re-entrant honeycomb structure incorporated bone plates serve as an effective bone design compared to the conventional bone plate design,in terms of stress shielding and intra-operative bending while offering similar mechanical and bending strength.

Design and test of a protective structure for the double vertical explosive welding of large titanium/steel plate

A comprehensive protective structure with rigidity and flexibility was put forward and designed in view of the quality and safety problems for the double vertical explosive welding of large titanium/steel cladding plate.The movement speed and displacement of the protective structure was calculated by establishing its physics model.The dynamics and stabilization properties were analyzed,and the protective structure parameters were optimized and devised.The comprehensive protective structure,which is composed of rigidity unit and flexibility wall,can bear the impact of detonation wave and the high-speed movement of the cladding plate.There are no damage and deformation in the protective structure and the cladding plate.The protective structure can be used many times.The bonding rate of the Ti/steel plate obtained was nearly 100%,and there is no deformation,surface cracks,and big wave and micro-defects.Therefore,the protective problems of the double vertical explosive welding can be solved effectively by the protective structure.

A novel multi-pin rectangular waveguide slow-wave structure based backward wave amplifier at 340 GHz

A backward wave amplifier（BWA） in a terahertz regime with a novel slow-wave structure（SWS） composed of multi parallel grating pins inside a rectangular waveguide is analyzed. The multi-pin rectangular waveguide SWS possesses good performance and is compatible with micro-fabrication technologies. The dispersion and interaction impedance of the multipin SWS are presented. The stopbands of the modes cling together in a Brillouim zone. The SWS has a high interaction impedance that is suitable for the interaction of multi cylindrical beams. The design, which is based on three parallel pins supporting the wave–beam interaction with four cylindrical beams, is verified by three-dimensional particle-in-cell simulations. A BWA with the central frequency at 340 GHz is demonstrated, and the output power is more than 100 mW.A tuning frequency range of 15 GHz（333–348 GHz） is obtained with a gain of more than 20 dB.

Density Structure of the Papua New Guinea-Solomon Arc Subduction System

The Papua New Guinea-Solomon(PN-SL)arc is one of the regions with active crustal motions and strong geological actions.Thus,its complex subduction system makes it an ideal laboratory for studying the initiation mechanism of plate subduction.However,the PN-SL subduction system has not yet been sufficiently studied,and its density structure has yet to be revealed.In this paper,we used the free-air gravity data,Parker-Oldenburg density surface inversion method,and the genetic algorithm density inversion method to obtain the density structure of an approximately 1000-km-long northwest-southeast line crossing the PN-SL subduction system under the constraints of the CRUST1.0 global crustal model,onshore seismic data,and the LLNL-G3Dv3 global P-wave velocity model.The density structure shows that density differences between the plates on the two sides of the trench could play a significant role in plate subduction.

Inverse Load Identification in Stiffened Plate Structure Based on in situ Strain Measurement

For practical engineering structures,it is usually difficult to measure external load distribution in a direct manner,which makes inverse load identification important.Specifically,load identification is a typical inverse problem,for which the models(e.g.,response matrix)are often ill-posed,resulting in degraded accuracy and impaired noise immunity of load identification.This study aims at identifying external loads in a stiffened plate structure,through comparing the effectiveness of different methods for parameter selection in regulation problems,including the Generalized Cross Validation(GCV)method,the Ordinary Cross Validation method and the truncated singular value decomposition method.With demonstrated high accuracy,the GCV method is used to identify concentrated loads in three different directions(e.g.,vertical,lateral and longitudinal)exerted on a stiffened plate.The results show that the GCV method is able to effectively identify multi-source static loads,with relative errors less than 5%.Moreover,under the situation of swept frequency excitation,when the excitation frequency is near the natural frequency of the structure,the GCV method can achieve much higher accuracy compared with direct inversion.At other excitation frequencies,the average recognition error of the GCV method load identification less than 10%.

Complicated deformation simulating on temperature-driven 4D printed bilayer structures based on reduced bilayer plate model

The four-dimensional(4D) printing technology, as a combination of additive manufacturing and smart materials, has attracted increasing research interest in recent years. The bilayer structures printed with smart materials using this technology can realize complicated deformation under some special stimuli due to the material properties.The deformation prediction of bilayer structures can make the design process more rapid and thus is of great importance. However, the previous works on deformation prediction of bilayer structures rarely study the complicated deformations or the influence of the printing process on deformation. Thus, this paper proposes a new method to predict the complicated deformations of temperature-sensitive 4D printed bilayer structures,in particular to the bilayer structures based on temperature-driven shape-memory polymers(SMPs) and fabricated using the fused deposition modeling(FDM) technology. The programming process to the material during printing is revealed and considered in the simulation model. Simulation results are compared with experiments to verify the validity of the method. The advantages of this method are stable convergence and high efficiency,as the three-dimensional(3D) problem is converted to a two-dimensional(2D) problem.The simulation parameters in the model can be further associated with the printing parameters, which shows good application prospect in 4D printed bilayer structure design.

A novel triple periodic minimal surface-like plate lattice and its data-driven optimization method for superior mechanical properties

Lattice structures can be designed to achieve unique mechanical properties and have attracted increasing attention for applications in high-end industrial equipment,along with the advances in additive manufacturing(AM)technologies.In this work,a novel design of plate lattice structures described by a parametric model is proposed to enrich the design space of plate lattice structures with high connectivity suitable for AM processes.The parametric model takes the basic unit of the triple periodic minimal surface(TPMS)lattice as a skeleton and adopts a set of generation parameters to determine the plate lattice structure with different topologies,which takes the advantages of both plate lattices for superior specific mechanical properties and TPMS lattices for high connectivity,and therefore is referred to as a TPMS-like plate lattice(TLPL).Furthermore,a data-driven shape optimization method is proposed to optimize the TLPL structure for maximum mechanical properties with or without the isotropic constraints.In this method,the genetic algorithm for the optimization is utilized for global search capability,and an artificial neural network(ANN)model for individual fitness estimation is integrated for high efficiency.A set of optimized TLPLs at different relative densities are experimentally validated by the selective laser melting(SLM)fabricated samples.It is confirmed that the optimized TLPLs could achieve elastic isotropy and have superior stiffness over other isotropic lattice structures.

Analysis of Dynamic Structure-Fluid Interaction Response of a Floating Laminated Composite Plate

In consideration of the effects of transverse shear deformation and structure-fluid interaction, the analytical expression of fluid force between a floating laminated composite plate and liquid surface is obtained. By expanding the displacements into Fourier series, the structure-fluid coupling dynamic response is solved. The effects of lamination angle, layer number, depth of fluid region and loading forms on dynamic response are investigated.

FLOW STRUCTURES AND FORCE CHARACTERISTICS FOR FLAT PLATE IN OSCILLATORY FLOWS WITH K_c NUMBER FROM 2 TO 40 AND IN COMBINED FLOWS

The evolution of wake structures and variation of the forces on a flat plate in harmonic oscillatory and in-line combined flows are obtained numerically by improved discrete vortex method. For the oscillatory oncoming flow cases, when K_c number varies from 2 to 40, the vortex pattern changes from a 'harmonic wave' shaped (in a range of small K_c numbers) to a slight inclined 'harmonic wave' shaped (in a range of moderate K_c numbers), then to inclined vortex clusters with an angle of 50 ° to the oncoming flow direction (at K_c = 20), at last, as K_c number becomes large, the vortex pattern is like a normal Karman vortex street. The well predicted drag and inertia force coefficients are obtained, which are more close to the results of Keulegan & Carpenter's experiment as compared with previous vortex simulation by other au- thors. The existence of minimum point of inertia force coefficient C_m near K_c = 20 is also well predicted and this phenomenon can be interpreted according to the vortex structure. For steady-oscillatory in-line combined flow cases, the vortex modes behave like a vortex street, exhibit a 'longitudinal wave' structure, and a vor- tex cluster shape corresponding to the ratios of U_m to U_0 which are of O (10^(-1)), O(1)and O (10), respectively. The effect on the prediction of forces on the flat plate from the disturbance component in a combined flow has been demon- strated qualitatively. In addition to this, the lock-in phenomenon of vortex shedding has been checked.

Optimization of the Water-Cooled Structure for the Divertor Plates in EAST Based on an Orthogonal Theory

An orthogoual experimental scheme was designed for optimizing a water-cooled structure of the divertor plate. There were three influencing factors： the radius R of the water- cooled pipe, and the pipe spacing L1 and L3. The influence rule of different factors on the cooling effect and thermal stress of the plate were studied, for which the influence rank was respectively R 〉 L1 〉 L3 and L3 〉 R 〉 L1. The highest temperature value decreased when R and L1 increased~ and the maximum thermal stress value dropped when R, L1 and L3 increased. The final optimized results can be summarized as： R equals 6 mm or 7 mm, L1 equals 19 mm, and L3 equals 20 mm. Compared with the initial design, the highest temperature value had a small decline~ and the maximum thermal stress value dropped by 19~ to 24~. So it was not ideal to improve the cooling effect by optimizing the geometry sizes of the water-cooled structure, even worse than increasing the flow speed, but it was very effective for dropping the maximum thermal stress value. The orthogoaal experimental method reduces the number of experiments by 80%, and thus it is feasible and effective to optimize the water-cooled structure of the divertor plate with the orthogonal theory.

Fluid-Structure Interaction Analysis of Flexible Plate with Partitioned Coupling Method

The development and rapid usage of numerical codes for fluid-structure interaction(FSI) problems are of great relevance to researchers in many engineering fields such as civil engineering and ocean engineering. This multidisciplinary field known as FSI has been expanded to engineering fields such as offshore structures, tall slender structures and other flexible structures applications. The motivation of this paper is to investigate the numerical model of two-way coupling FSI partitioned flexible plate structure under fluid flow. The adopted partitioned method and approach utilized the advantage of the existing numerical algorithms in solving the two-way coupling fluid and structural interactions. The flexible plate was subjected to a fluid flow which causes large deformation on the fluid domain from the oscillation of the flexible plate. Both fluid and flexible plate are subjected to the interaction of load transfer within two physics by using the strong and weak coupling methods of MFS and Load Transfer Physics Environment, respectively. The oscillation and deformation results have been validated which demonstrate the reliability of both strong and weak method in resolving the two-way coupling problem in contribution of knowledge to the feasibility field study of ocean engineering and civil engineering.

STOCHASTIC BOUNDARY ELEMENT METHOD FOR RELIABILITY ANALYSIS OF PLATE AND BEAMS COMPOSITE STRUCTURES

In this paper, the reliability of orthotropic plate and beams composite structures, which is under the actions of the stochastic loading and stochastic boundary conditions, have been analyzed by stochastic boundary element method. First, the boundary integral equation of orthotropic plate and beams composite structures is given in this paper, and then based on the stochastic boundary element method, the method for reliability analysis of stochastic structures is establishes and formulas for computation of reliability index of orthotropic plate and beams composite structures are obtained. The computed examples show the efficient of the method used in this paper.

Effect of cooling structure on thermal behavior of copper plates of slab continuous casting mold

A three-dimensional finite-element model of slab continuous casting mold was conducted to clarify the effect of cooling structure on thermal behavior of copper plates. The results show that temperature distribution of hot surface is mainly governed by cooling structure and heat-transfer conditions. For hot surface centricity, maximum surface temperature promotions are 30℃ and 15℃ with thickness increments of copper plates of 5 mm and nickel layers of 1 mm, respectively. The surface temperature without nickel layers is depressed by 10℃ when the depth increment of water slots is 2 mm and that with nickel layers adjacent to and away from mold outlet is depressed by 7℃ and 5℃, respectively. The specific trend of temperature distribution of transverse sections of copper plates is nearly free of cooling structure, but temperature is changed and its law is similar to the corresponding surface temperature.

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.

Fine structure characterization of an explosively-welded GH3535/316H bimetallic plate interface

An explosion-welded technology was induced to manufacture the GH3535/316H bimetallic plates to provide a more cost-effective structural material for ultrahigh temperature,molten salt thermal storage systems.The microstructure of the bonding interfaces were extensively investigated by scanning electron microscopy,energy dispersive spectrometry,and an electron probe microanalyzer.The bonding interface possessed a periodic,wavy morphology and was adorned by peninsula-or island-like transition zones.At higher magnification,a matrix recrystallization region,fine grain region,columnar grain region,equiaxed grain region,and shrinkage porosity were observed in the transition zones and surrounding area.Electron backscattered diffraction demonstrated that the strain in the recrystallization region of the GH3535 matrix and transition zone was less than the substrate.Strain concentration occurred at the interface and the solidification defects in the transition zone.The dislocation substructure in 316H near the interface was characterized by electron channeling contrast imaging.A dislocation network was formed in the grains of 316H.The microhardness decreased as the distance from the welding interface increased and the lowest hardness was inside the transition zone.