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.

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.

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%.

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.

Reconstruction Technology of Flexible Structure Shape Based on FBG Sensor Array and Deep Learning Algorithm

A structural displacement field reconstruction method is proposed to aim at the problems of deformation mon-itoring and displacement field reconstruction of flexible plate-like structures in the aerospace field.This method combines the deep neural network model of the cross-layer connection structure with the fiber grating sensor network.This paper first introduces the principle of strain detection of fiber grating sensor,studies the mapping relationship between strain and displacement,and proposes a strain-displacement conversion model based on an improved neural network.Then the intelligent structure deformation monitoring system is built.By controlling the stepping distance of the motor to produce different deformations of the plate structure,the strain information and real displacement information are obtained based on the high-density fiber grating sensor network and the dial indicator array.Finally,based on the deformation prediction model obtained by training,the displacement field reconstruction of the structure under different deformation states is realized.Experimental results show that the mean absolute error of the deformation of the measuring points obtained by this method is less than 0.032 mm.This method is feasible in theory and practice and can be applied to the deformation monitoring of aerospace vehicle structures.

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.

基于TLBO算法的不确定性条件下复杂产品协同设计的可靠性拓扑优化

复杂产品的拓扑优化设计可以显著节省材料和节能,有效地降低惯性力和机械振动。本研究以一种大吨位液压机作为典型的复杂产品,用于阐述该优化方法。本文提出了一种基于可靠性与优化解耦模型和基于教学学习的优化(TLBO)算法的可靠性拓扑优化方法。将由板结构形成的支撑物作为拓扑优化对象,重量轻、稳定性好。将不确定性下的可靠性优化和结构拓扑优化协同处理。首先,利用有限差分法将优化问题中的不确定性参数修正为确定性参数。然后,将不确定性可靠性分析和拓扑优化的复杂嵌套解耦。最后,利用TLBO算法求解解耦模型,该算法参数少,求解速度快。TLBO算法采用了自适应教学因子,在初始阶段实现了更快的收敛速度,并在后期进行了更精细的搜索。本文给出了一个液压机基板结构的数值实例,说明了该方法的有效性。

Perpendicular intergrowth ZSM-5 plates with shortened 10-MR pores

ZSM-5 plates with a perpendicular intergrowth structure was synthesized by using a simple amine as the structure directing agent under hydrothermal conditions,in which the mother plate and the perpendicularly standing plates oriented along the(010)and(100)planes of MFI crystals,respectively.During the crystallization process,the mother plate was initially formed on the surface of the amorphous solid gel,while a set of parallel plates perpendicularly grew on its surface,via a homogeneous nucleation mechanism.The mother plate and the perpendicular plates had a similar thickness of 100-200 nm and were characterized by considerably shortened straight and zigzag 10 member ring pores,respectively.This unique intergrowth structure greatly facilitated the diffusion of the reactive molecules in HZSM-5 crystals during methanol conversion to hydrocarbons.

Numerical simulation for deformation of multi-layer steel plates under underwater impulsive loading

To further understand the dynamic deformation and impact resistance of thin-plate hull structure under impulse wave,the deformation of multi-layer steel plates under underwater impulsive loading has been studied by AUTODYN V6.1.In order to verify the validity of numerical methods,the experimental results are compared with the simulation results.The multi-layer plate types include 1 mm + 3 mm,2 mm + 2 mm,3 mm + 1 mm double-layer,and 4 mm monolayer annealed 304 stainless steel plates.Each type of target plates has four flyer plate's velocities.There are 150,200,250 m /s and 300 m /s.The pressure wave histories in water and deformation of specimens have been predicted and measured by numerical simulations.The simulation results demonstrate that the protective capacity of 2mm + 2mm double-layer annealed 304 stainless steel plates is the best one in this velocity range of flyer plate,as the integral deformation is the smallest among the four structure types.

Ultimate Compressive Strength Computational Modeling for Stiffened Plate Panels with Nonuniform Thickness

The aim of this paper is to develop computational models for the ultimate compressive strength analysis of stiffened plate panels with nonuniform thickness.Modeling welding-induced initial deformations and residual stresses was presented with the measured data.Three methods,i.e.,ANSYS finite element method,ALPS/SPINE incremental Galerkin method,and ALPS/ULSAP analytical method,were employed together with existing test database obtained from a full-scale collapse testing of steel-stiffened plate structures.Sensitivity study was conducted with varying the difference in plate thickness to define a representative(equivalent)thickness for plate panels with nonuniform thickness.Guidelines are provided for structural modeling to compute the ultimate compressive strength of plate panels with variable thickness.

THEORY OF ELASTICITY OF AN ANISOTROPIC BODY FOR THE BENDING OF BEAMS

A theory of elasticity for the bending of orthogonal anisotropic beams was developed in this paper by analogy with the special case, which can be obtained by applying the theory of elasticity for bending of transversely isotropic plates to the problems of two dimensions. The authors also presented a method to solve the problems of bending of orthogonal anisotropic beams and a new theory of the deep-beam whose ratio of depth to length is larger. It is pointed out that Reissner's theory which takes into account the effect of transverse shear deformation is not suitable for the components of stress in our case.

Analysis of nonlinear vibration for symmetric angle-ply laminated viscoelastic plates with damage

The behavior of nonlinear vibration for symmetric angle-ply laminated plates including the material viscoelasticity and damage evolution is investigated. By employing the von Karman＇s nonlinear theory, strain energy equivalence principle and Boltzmann superposition principle, a set of governing equations of nonlinear integro-differential type are derived. By applying the finite difference method, Newmark method and iterative procedure, the governing equations are solved. The effects of loading amplitudes, exciting frequencies and different ply orientations on the critical time to failure initiation and nonlinear vibration amplitudes of the structures are discussed. Numerical results are presented for the different parameters and compared with the available data.

PERTURBATION SOLUTION FOR THERMAL EXPANSION BUCKLING OF NO EXPANSION JOINT SLOPE PAVEMENT PLATE

The mechanical mechanism of thermal expansion buckling of no expansion joint slope pavement undergoing the action of a temperature field was analyzed. By using the regular perturbation method, the formula of perturbation solution for this problem was derived, the relationship between critical laying temperature difference of slope pavement and of level straight pavement was studied, and the unified solution as well as its numerical results was also obtained. In terms of this research, the reasonable laying temperature of no expansion joint slope pavement was given.

RESEARCH ON DYNAMIC BEHAVIOUR AND NOISE REDUCTION OF METAL CUTTING SAW PLATES

Based upon theoretical and experimental methods of acoustics and vibration, the dynamic characteristics of cutting processes have been researched systematically, and a simplified method of quickly estimating the modal parameters of elastic circular plate structures under clamping has also been advanced. Furthermore, we try the best to explore effectively the noise-reducing ways in the sawing process. In fact, satisfactory results have been achieved in practice.

ON THE STABILITY ANALYSIS OF PLATES AND SHELLS USING A QUADRILATERAL,16-DEGREES OF FREEDOM PLAT SHELL ELEMENT DKQ16

The linear buckling problems of plates and shells were analysed using a recently developped quadrilateral,16-degrees of freedom flat shell element (called DKQ16).The geometrical stiffness matrix was established.Comparison of the numerical results for several typical problems shows that the DKQ16 element has a very good precision for the linear buckling problems of plates and shells.

P-FEMOL ANALYSIS OF PLATE BENDING PROBLEMS

In this paper, the p- version of the finite element method of lines (FEMOL) for the analysis of the Mindlin-Reissner plate bending problems is presented and a class of p-FEMOL elements with polynomial degrees as high as nine is developed. Numerical examples given in this paper show tremendous performance of the present method: namely, rapid convergence rate, high accuracy for both displacements and stress resultants, removal of shear-locking trouble, capability of dealing with difficult problems such as the boundary layer behavior near a free edge and stress concentration around a hole.

MECHANICAL VIBRATIONAL POWER FLOW IN BEAM-PLATE ASSEMBLIES

The vibrational power flow in the beam-plate assemblies and then with the isolators is investigated using analytical ' power flow' approach based on the some concepts of mechanical mo- bility and structural dynamics. Theoretical expressions of the power flow in the structures are given and examined. The numerical results of the expressions are good agreements with the measuring re- sults obtained by the technique of vibration intensity. On the basis of these results, possible ways of reducing the vibrational power flow in the structures are suggested .

Cooling System Design and Thermal Analysis of Modular Stator Hybrid Excitation Synchronous Motor

Hybrid excitation synchronous motor has the advantages of uniform and adjustable electromagnetic field, wide speed range and high power density. It has broad application prospects in new energy electric vehicles, wind power generation and other fields. This paper introduces the basic structure of hybrid excitation motor with modular stator, and analyzes the operation principle of hybrid excitation motor. The cooling structure of the water-cooled plate is designed, and the effects of the thickness of the water-cooled plate and the number of water channels in the water-cooled plate on the heat dissipation capacity of the water-cooled plate are analyzed by theoretical and computational fluid dynamics methods. The effects of different water cooling plate structures on water velocity, pressure drop, water pump power consumption and heat dissipation capacity were compared and analyzed. The influence of different inlet flow velocity on the maximum temperature rise of each part of the motor is analyzed, and the temperature of each part of the motor under the optimal water flow is analyzed. The influence of the traditional spiral water jacket cooling structure and the water-cooled plate cooling structure on the maximum temperature rise of the motor components is compared and analyzed. The results show that the water-cooled plate cooling structure is more suitable for the modular stator motor studied in this paper. Based on the water-cooled plate cooling structure, the air-water composite cooling structure is designed, and the effects of the air-water composite cooling structure and the water-cooled plate cooling structure on the maximum temperature rise of each component of the motor are compared and analyzed. The results show that the maximum temperature rise of each component of the motor is reduced under the air-water composite cooling structure.

Topology optimization of plate structures using plate element-based moving morphable component(MMC)approach

A topology optimization approach for designing the layout of plate structures is proposed in this article.In this approach,structural mechanical behavior is analyzed under the framework of Kirchhoff plate theory,and structural topology is described explicitly by a set of moving morphable components.Compared to the existing treatments where structural topology is generally described in an implicit manner,the adopted explicit geometry/layout description has demonstrated its advantages on several aspects.Firstly,the number of design variables is reduced substantially.Secondly,the obtained optimized designs are pure black-and-white and contain no gray regions.Besides,numerical experiments show that the use of Kirchhoff plate element helps save 95-99%computational time,compared with traditional treatments where solid elements are used for finite element analysis.Moreover the accuracy of the proposed method is also validated through a comparison with the corresponding theoretical solutions.Several numerical examples are also provided to demonstrate the effectiveness of the proposed approach.