scholarly journals Concurrent Topology Optimization of Composite Plates for Minimum Dynamic Compliance

Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 538
Author(s):  
Heng Zhang ◽  
Xiaohong Ding ◽  
Weiyu Ni ◽  
Yanyu Chen ◽  
Xiaopeng Zhang ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Frequency Response ◽  
Composite Plates ◽  
Dynamic Compliance ◽  
Superposition Method ◽  
Complex Frequency ◽  
Concurrent Topology Optimization ◽  
Periodic Composites ◽  
Mode Superposition Method ◽  
Design Variables

This paper proposes a novel density-based concurrent topology optimization method to support the two-scale design of composite plates for vibration mitigation. To have exceptional damping performance, dynamic compliance of the composite plate is taken as the objective function. The complex stiffness model is used to describe the material damping and accurately consider the variation of structural response due to the change of damping composite material configurations. The mode superposition method is used to calculate the complex frequency response of the composite plates to reduce the heavy computational burden caused by a large number of sample points in the frequency range during each iteration. Both microstructural configurations and macroscopic distribution are optimized in an integrated manner. At the microscale, the damping layer consists of periodic composites with distinct damping and stiffness. The effective properties of the periodic composites are homogenized and then are fed into the complex frequency response analysis at the macroscale. To implement the concurrent topology optimization at two different scales, the design variables are assigned for both macro- and micro-scales. The adjoint sensitivity analysis is presented to compute the derivatives of dynamic compliance of composite plates with respect to the micro and macro design variables. Several numerical examples with different excitation inputs and boundary conditions are presented to confirm the validity of the proposed methodologies. This paper represents a first step towards designing two-scale composite plates with optional dynamic performance under harmonic loading using an inverse design method.

scholarly journals Topology Optimization of Hard-Coating Thin Plate for Maximizing Modal Loss Factors

Coatings ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 774
Author(s):  
Haitao Luo ◽  
Rong Chen ◽  
Siwei Guo ◽  
Jia Fu
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Composite Plates ◽  
Optimization Method ◽  
Hard Coating ◽  
Design Variables ◽  
Coating Composite ◽  
Damping Materials ◽  
Topology Optimization Method ◽  
Loss Factors

At present, hard coating structures are widely studied as a new passive damping method. Generally, the hard coating material is completely covered on the surface of the thin-walled structure, but the local coverage cannot only achieve better vibration reduction effect, but also save the material and processing costs. In this paper, a topology optimization method for hard coated composite plates is proposed to maximize the modal loss factors. The finite element dynamic model of hard coating composite plate is established. The topology optimization model is established with the energy ratio of hard coating layer to base layer as the objective function and the amount of damping material as the constraint condition. The sensitivity expression of the objective function to the design variables is derived, and the iteration of the design variables is realized by the Method of Moving Asymptote (MMA). Several numerical examples are provided to demonstrate that this method can obtain the optimal layout of damping materials for hard coating composite plates. The results show that the damping materials are mainly distributed in the area where the stored modal strain energy is large, which is consistent with the traditional design method. Finally, based on the numerical results, the experimental study of local hard coating composites plate is carried out. The results show that the topology optimization method can significantly reduce the frequency response amplitude while reducing the amount of damping materials, which shows the feasibility and effectiveness of the method.

Coating position optimization for a hard-coating thin-plate structure based on resonance response

2020 ◽  
pp. 1-15
Author(s):  
Wei Sun ◽  
Yue Sun ◽  
Rong Liu
Keyword(s):  
Thin Plate ◽  
Hard Coating ◽  
Superposition Method ◽  
Analysis Model ◽  
Optimal Position ◽  
Mode Superposition Method ◽  
Design Variables ◽  
Resonance Response ◽  
Design Requirements ◽  
Population Genetic Algorithm

The ultimate goal of vibration reduction using hard coating is to suppress the resonance peaks of the structure. Thus, the optimal position of the coating as a function of the resonance response will better satisfy the design requirements. Based on a full consideration of the continuous coating area, a method for optimizing the coating position with the objective of minimizing resonance response was developed for the hard-coating thin plate. A semi-analytical analysis model of the partially coated cantilever thin plate was created, and the formula for solving the vibration response was identified by the mode superposition method. An optimization model was established. In the model, the position coordinates of coating patches are the design variables, and the objective function is the maximizing of the reciprocals of the resonance peaks, which is equivalent to minimizing the resonance response. A multi-population genetic algorithm (MPGA) has been proposed to solve the coating position optimization problem. Finally, a cantilever titanium plate coated with NiCrAlCoY + YSZ hard coating was chosen to demonstrate the presented method. The results show that the obtained optimized results can guarantee that the resonance peaks of the hard-coating thin plate are always less than those of general cases, whether it is for single-order or multi-order optimization objectives.

Layout design of piezoelectric patches in structural linear quadratic regulator optimal control using topology optimization

2018 ◽  
Vol 29 (10) ◽  
pp. 2277-2294 ◽  
Author(s):  
Jun Hu ◽  
Xiaopeng Zhang ◽  
Zhan Kang
Keyword(s):  
Optimal Control ◽  
Topology Optimization ◽  
Linear Quadratic Regulator ◽  
Lyapunov Equation ◽  
Dynamic Compliance ◽  
Layout Design ◽  
Control Performance ◽  
Linear Quadratic ◽  
Structural Dynamic ◽  
Design Variables

This article investigates topology optimization for piezoelectric thin-shell structures under the linear quadratic regulator optimal control. In the optimization model, the structural dynamic compliance is taken as the measure of control performance, and the relative densities describing the distribution of the piezoelectric material are considered as design variables. An artificial material model with penalization on both mechanical and piezoelectric properties is employed. For the purpose of improving computational efficiency of the sensitivity and response analysis, modal superposition method is adopted. The derivative of the Riccati equation governing the linear quadratic regulator control with respect to the design variables is shown to be a Lyapunov equation. In conjunction with the adjoint variable method, the design sensitivities of the dynamic compliance are obtained using the solution of the Lyapunov equation. Numerical examples demonstrate the validity of the proposed method and show the significance of layout design of piezoelectric sensors/actuators. The influences of some key factors on the optimization solutions are discussed. It is shown that the optimized layout of the piezoelectric patches may be significantly influenced by the excitation frequency, but only slightly affected by the choice of the weighting matrix in the linear quadratic regulator control. This work aims to provide an efficient gradient-based mathematical programming method for guiding the layout design of actuators and sensors in smart structures under optimal vibration control. However, the considered model is a purely mathematical one without consideration of engineering realization, thus the optimization result may only serve as an upper bound for practically realizable control performance.

scholarly journals A Sequential Approach for Aerodynamic Shape Optimization with Topology Optimization of Airfoils

2021 ◽  
Vol 26 (2) ◽  
pp. 34
Author(s):  
Isaac Gibert Martínez ◽  
Frederico Afonso ◽  
Simão Rodrigues ◽  
Fernando Lau
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Volume Fraction ◽  
Optimization Techniques ◽  
Free Form ◽  
Aerodynamic Shape Optimization ◽  
Sequential Approach ◽  
Airfoil Surface ◽  
Aerodynamic Shape ◽  
Design Variables

The objective of this work is to study the coupling of two efficient optimization techniques, Aerodynamic Shape Optimization (ASO) and Topology Optimization (TO), in 2D airfoils. To achieve such goal two open-source codes, SU2 and Calculix, are employed for ASO and TO, respectively, using the Sequential Least SQuares Programming (SLSQP) and the Bi-directional Evolutionary Structural Optimization (BESO) algorithms; the latter is well-known for allowing the addition of material in the TO which constitutes, as far as our knowledge, a novelty for this kind of application. These codes are linked by means of a script capable of reading the geometry and pressure distribution obtained from the ASO and defining the boundary conditions to be applied in the TO. The Free-Form Deformation technique is chosen for the definition of the design variables to be used in the ASO, while the densities of the inner elements are defined as design variables of the TO. As a test case, a widely used benchmark transonic airfoil, the RAE2822, is chosen here with an internal geometric constraint to simulate the wing-box of a transonic wing. First, the two optimization procedures are tested separately to gain insight and then are run in a sequential way for two test cases with available experimental data: (i) Mach 0.729 at α=2.31°; and (ii) Mach 0.730 at α=2.79°. In the ASO problem, the lift is fixed and the drag is minimized; while in the TO problem, compliance minimization is set as the objective for a prescribed volume fraction. Improvements in both aerodynamic and structural performance are found, as expected: the ASO reduced the total pressure on the airfoil surface in order to minimize drag, which resulted in lower stress values experienced by the structure.

scholarly journals Transient Response of Bridge Piers to Structure Separation under Near-Fault Vertical Earthquake

2021 ◽  
Vol 11 (9) ◽  
pp. 4068
Author(s):  
Wenjun An ◽  
Guquan Song
Keyword(s):  
Large Scale ◽  
Bending Moment ◽  
Relative Displacement ◽  
Superposition Method ◽  
Longitudinal Displacement ◽  
Transient Wave ◽  
Vibration Period ◽  
Vertical Excitation ◽  
Mode Superposition Method ◽  
Main Girder

Given the possible separation problem caused by the double-span continuous beam bridge under the action of the vertical earthquake, considering the wave effect, the transient wave characteristic function method and the indirect mode superposition method are used to solve the response theory of the bridge structure during the earthquake. Through the example analysis, the pier bending moment changes under different vertical excitation periods and excitation amplitudes are calculated. Calculations prove that: (1) When the seismic excitation period is close to the vertical natural vibration period of the bridge, the main girder and the bridge pier may be separated; (2) When the pier has a high height, the separation has a more significant impact on the longitudinal displacement of the bridge, but the maximum relative displacement caused by the separation is random; (3) Large-scale vertical excitation will increase the number of partitions of the structure, and at the same time increase the vertical collision force between the main girder and the pier, but the effect on the longitudinal displacement of the form is uncertain; (4) When V/H exceeds a specific value, the pier will not only be damaged by bending, but will also be damaged by axial compression.

Numerical Experiments in Using Voronoi Cell Finite Elements for Topology Optimization

2009 ◽  
Author(s):  
James M. Gibert ◽  
Georges M. Fadel
Keyword(s):  
Topology Optimization ◽  
Isotropic Material ◽  
Numerical Experiments ◽  
Voronoi Cell ◽  
Material Model ◽  
Topological Optimization ◽  
Advantages And Disadvantages ◽  
Compliance Minimization ◽  
Design Variables ◽  
Standard Linear

This paper provides two separate methodologies for implementing the Voronoi Cell Finite Element Method (VCFEM) in topological optimization. Both exploit two characteristics of VCFEM. The first approach utilizes the property that a hole or inclusion can be placed in the element: the design variables for the topology optimization are sizes of the hole. In the second approach, we note that VCFEM may mesh the design domain as n sided polygons. We restrict our attention to hexagonal meshes of the domain while applying Solid Isotropic Material Penalization (SIMP) material model. Researchers have shown that hexagonal meshes are not subject to the checker boarding problem commonly associated with standard linear quad and triangle elements. We present several examples to illustrate the efficacy of the methods in compliance minimization as well as discuss the advantages and disadvantages of each method.

Efficient Sensitivity Analysis for Multibody Dynamics Systems Using an Iterative Steps Method With Application in Topology Optimization

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi ◽  
Sudhakar Arepally ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Multibody Dynamics ◽  
Optimization Problem ◽  
Finite Difference Methods ◽  
Analysis Method ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Rotational Motions

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

Structural Analysis and Optimal Design of Lightweight Skate for Loading and Unloading

2013 ◽  
Vol 785-786 ◽  
pp. 1258-1261
Author(s):  
In Pyo Cha ◽  
Hee Jae Shin ◽  
Neung Gu Lee ◽  
Lee Ku Kwac ◽  
Hong Gun Kim
Keyword(s):  
Topology Optimization ◽  
Structural Analysis ◽  
Optimal Design ◽  
Optimization Techniques ◽  
Normal Operation ◽  
Stress And Strain ◽  
Initial Model ◽  
Design Variables ◽  
Model Set ◽  
Main Frame

Topology optimization and shape optimization of structural optimization techniques are applied to transport skate the lightweight. Skate properties by varying the design variables and minimize the maximum stress and strain in the normal operation, while reducing the volume of the objective function of optimal design and Skate the static strength of the constraints that should not degrade compared to the performance of the initial model. The skates were used in this study consists of the main frame, sub frame, roll, pin main frame only structural analysis and optimal design was performed using the finite element method. Simplified initial model set design area and it compared to SM45C, AA7075, CFRP, GFRP was using the topology optimization. Strength does not degrade compared to the initial model, decreased volume while minimizing the stress and strain results, the optimum design was achieved efficient lightweight.

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