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.

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%.

Constructal design method dealing with stiffened plates and symmetry boundaries

A new computational procedure for modelling the structural behavior of stiffened plates with symmetry boundary conditions is here presented.It uses two-dimensional finite elements as a way to decrease computational time without losing precision thanks to a relatively small number of elements applied for analyzing out-of-plane displacements(deflections)and stresses.Adding,the constructal design method was included in the procedure,together with the exhaustive search technique,with the scope to optimize the stress/strain status of stiffened plates by design changes.For the purpose,a reference plate without stiffeners was initially design and used as starting point.Part of the volume was reshaped into stiffeners:thickness was reduced maintaining unchanged weight,length and width.The main goal was to minimize strains and stresses by geometric changes.Results demonstrated that,thanks to this design procedure,it is always possible to find an adequate geometry transformation from reference plate into stiffeners,allowing significant improvements in mechanical behavior.

Bandgap formation and low-frequency structural vibration suppression for stiffened plate-type metastructure with general boundary conditions

Metastructures with unique mechanical properties have shown attractive potential application in vibration and noise reduction.Typically,most of the metastructures deal with the vibration bandgap properties of infinite structures without considering specific boundary condition and dynamic behaviors,which cannot be directly applied to the engineering structures.In this research,we design a Stiffened Plate-type Metastructure(SPM)composed of a plate with periodic stiffeners and cantilever beam-type resonators subjected to general boundary conditions for low-frequency vibration suppression.The effects of boundary conditions and the number and orientation of the stiffeners on Locally Resonant(LR)type bandgap properties in SPM are further investigated.An analytical modeling framework is developed to predict the bandgap formations and vibration behaviors of SPMs in finite-size configuration.The governing equations of the SPM reinforced by various arrangements of stiffeners are derived based on the first-order shear deformation theory and Hamilton’s principle,and a Fourier series combined with auxiliary functions is employed to satisfy the arbitrary boundary conditions.Finite element analysis and experimental investigations of vibration behaviors for the SPM are carried out to validate the accuracy and reliability of the present analytical model.For practical designs of the SPMs with specific boundary conditions,it is found that there exist optimal numbers of stiffeners and resonators which can produce the significant LR-type bandgap behaviors.Furthermore,various arrangements of stiffeners and resonators are explored for different boundary conditions by breaking the requirement of spatially periodicity.It is shown that for the designed SPM,the vibration modes of its host structure should be considered to widen the frequency range in which the resonators transfer and store energy,and hence improve the performance of low-frequency vibration suppression.The present work can provide a significant theoretical guidance for the engineering application of metamaterial stiffened structures。

B-Spline Wavelet on Interval Finite Element Method for Static and Vibration Analysis of Stiffened Flexible Thin Plate

A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and virtual work principle,the formulations of the bending and free vibration problems of the stiffened plate are derived separately.Then,the scaling functions of the B-spline wavelet on the interval(BSWI)are introduced to discrete the solving field variables instead of conventional polynomial interpolation.Finally,the corresponding two problems can be resolved following the traditional finite element frame.There are some advantages of the constructed elements in structural analysis.Due to the excellent features of the wavelet,such as multi-scale and localization characteristics,and the excellent numerical approximation property of the BSWI,the precise and efficient analysis can be achieved.Besides,transformation matrix is used to translate the meaningless wavelet coefficients into physical space,thus the resolving process is simplified.In order to verify the superiority of the constructed method in stiffened plate analysis,several numerical examples are given in the end.

Impact Damage Identification of Aluminum Alloy Reinforced Plate Based on GWO-ELM Algorithm

As a critical structure of aerospace equipment,aluminum alloy stiffened plate will influence the stability of spacecraft in orbit and the normal operation of the system.In this study,a GWO-ELM algorithm-based impact damage identification method is proposed for aluminum alloy stiffened panels to monitor and evaluate the damage condition of such stiffened panels of spacecraft.Firstly,together with numerical simulation,the experimental simulation to obtain the damage acoustic emission signals of aluminum alloy reinforced panels is performed,to establish the damage data.Subsequently,the amplitude-frequency characteristics of impact damage signals are extracted and put into an extreme learning machine(ELM)model to identify the impact location and damage degree,and the Gray Wolf Optimization(GWO)algorithm is employed to update the weight parameters of the model.Finally,experiments are conducted on the irregular aluminum alloy stiffened plate with the size of 2200 mm×500 mm×10 mm,the identification accuracy of impact position and damage degree is 98.90% and 99.55% in 68 test areas,respectively.Comparative experiments with ELM and backpropagation neural networks(BPNN)demonstrate that the impact damage identification of aluminum alloy stiffened plate based on GWO-ELM algorithm can serve as an effective way to monitor spacecraft structural damage.

海洋管状结构轴向荷载下K型接头与外板局部节点柔度的数值分析与讨论

The Local Joint Flexibility(_(LJF))of steel K-joints reinforced with external plates under axial loads is investigated in this paper.For this aim,firstly,a finite element(FE)model was produced and verified with the results of several experimental tests.In the next step,a set of 150 FE models was generated to assess the effect of the brace angle(θ),the stiffener plate size(ηandλ),and the joint geometry(γ,τ,ξ,andβ)on the_(LJF)factor(f_(LJF)).The results showed that using the external plates can decrease 81%of the f_(LJF).Moreover,the reinforcing effect of the reinforcing plate on the f_(LJF)is more remarkable in the joints with smallerβ.Also,the effect of theγon the f_(LJF)ratio can be ignored.Despite the important effect of the f_(LJF)on the behavior of tubular joints,there is not available any study or equation on the f_(LJF)in any reinforced K-joints under axial load.Consequently,using the present FE results,a design parametric equation is proposed.The equation can reasonably predict the f_(LJF)in the reinforced K-joints under axial load.

Concurrent topology optimization design of stiffener layout and cross-section for thin-walled structures

Stiffened plates or shells are widely used in engineering structures as primary or secondary load-bearing components.How to design the layout and sizes of the stiffeners is of great significance for structural lightweight.In this work,a new topology optimization method for simultaneously optimizing the layout and cross-section topology of the stiffeners is developed to solve this issue.The stilfeners and base plates are modeled by the beam and shell elements,respectively,significantly reducing the computational cost.The Giavotto beam theory,instead of the widely employed Euler or Timoshenko beam theory,is applied to model the stiffeners for considering the warping deformation in evaluating the section stiffness of the beam.A multi-scale topology optimization model is established by simultaneously optimizing the layout of the beam and the topology of the cross-section.The design space is significantly expanded by optimizing these two types of design variables.Several numerical examples are applied to illustrate the validity and effectiveness of the proposed method.The results show that the proposed two-scale optimization approach can generate better designs than the single-scale method.