Topology Optimization of Blank Geometry for the Sheet Forming Process

2012 ◽  
Author(s):  
Saber DorMohammadi ◽  
Mohammad Rouhi ◽  
Masoud Rais-Rohani
Keyword(s):  
Topology Optimization ◽  
Volume Fraction ◽  
Structural Response ◽  
Sheet Forming ◽  
Forming Process ◽  
Exchange Method ◽  
Forming Simulation ◽  
Blank Shape Optimization ◽  
Blank Shape ◽  
Consistent Subset

The newly developed element exchange method (EEM) for topology optimization is applied to the problem of blank shape optimization for the sheet-forming process. EEM uses a series of stochastic operations guided by the structural response of the model to switch solid and void elements in a given domain to minimize the objective function while maintaining the specified volume fraction. In application of EEM to blank optimization, a sheet forming simulation model is developed using Abaqus/Explicit. With the goal of minimizing the variability in wall thickness of the formed component, a subset of solid (i.e., high density) elements with the highest increase in thickness is exchanged with a consistent subset of void (i.e., low density) elements having the highest decrease in thickness so that the volume fraction remains constant. The EEM operations coupled with finite element simulations are repeated until the optimum blank geometry (i.e., boundary and initial thickness) is found. The developed numerical framework is applied to blank optimization of a benchmark problem. The results show that EEM is successful in generating the optimum blank geometry efficiently and accurately.

Material microstructure topology optimization of piezoelectric composite beam under initial disturbance for vibration suppression

2021 ◽  
pp. 107754632199333
Author(s):  
Haoqing Ding ◽  
Bin Xu
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Optimization Model ◽  
Composite Beam ◽  
Volume Fraction ◽  
Structural Response ◽  
Initial Disturbance ◽  
Piezoelectric Composite ◽  
Material Microstructure ◽  
Time Integral

This study proposes a material microstructure topology optimization model for a piezoelectric composite beam subject to initial disturbance. The optimization model is built through the Solid Isotropic Material with Penalization interpolation subject to the material volume fraction on the microlevel. And the objective function is to minimize the time integral about local structural response. By introducing the Lyapunov second equation, this time integral is simplified and does not need any numerical integration technique. It can also be used to measure the global vibration response instead of short time gap. Besides, different objectives such as a regional structural response can also be obtained by only changing the weight matrix form. And the sensitivity of the objective function with respect to the design variables are also deduced by solving the Lyapunov equation. A bidirectional evolutionary structural optimization algorithm is used to acquire the optimal results. Four numerical examples including multiphase material microstructure topology optimization verify the developed method that can effectively suppress local structural vibration level and obtain lighter structure.

Blank shape optimization in the deep drawing process by sun method

2021 ◽  
Author(s):  
Hamidreza Gharehchahi ◽  
Mohammad Javad Kazemzadeh-Parsi ◽  
Ahmad Afsari ◽  
Mehrdad Mohammadi
Keyword(s):  
Shape Optimization ◽  
Deep Drawing ◽  
Drawing Process ◽  
Deep Drawing Process ◽  
Blank Shape Optimization ◽  
Blank Shape

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 Topology optimized thermoelectric generator: a parametric study

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
John Mativo ◽  
Kevin Hallinan ◽  
Uduak George ◽  
Greg Reich ◽  
Robin Steininger
Keyword(s):  
Topology Optimization ◽  
Thermoelectric Generator ◽  
Volume Fraction ◽  
Power Conversion ◽  
Power Production ◽  
Power Reduction ◽  
Void Volume Fraction ◽  
Thermoelectric Generators ◽  
Maximal Power ◽  
Design Yield

Abstract Typical thermoelectric generator legs are brittle which limits their application in vibratory and shear environments. Research is conducted to develop compliant thermoelectric generators (TEGs) capable of converting thermal loads to power, while also supporting shear and vibratory loads. Mathematical structural, thermal, and power conversion models are developed. Topology optimization is employed to tailor the TEG design yield maximal power production while sustaining the applied shear and vibratory loads. As a specific example, results are presented for optimized TEG legs with a void volume fraction of 0.2 that achieve compliance shear displacement of 0.0636 (from a range of 0.0504 to 0.6079). In order to achieve the necessary compliance to support the load, the power reduction is reduced by 20% relative to similarly sized void free TEG legs.

scholarly journals Buckling Behavior of FG-CNT Reinforced Composite Conical Shells Subjected to a Combined Loading

Nanomaterials ◽  
2020 ◽  
Vol 10 (3) ◽  
pp. 419 ◽  
Author(s):  
Abdullah H. Sofiyev ◽  
Francesco Tornabene ◽  
Rossana Dimitri ◽  
Nuri Kuruoglu
Keyword(s):  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Structural Response ◽  
Systematic Investigation ◽  
Functionally Graded ◽  
Combined Loading ◽  
Proportional Loading ◽  
Conical Shells ◽  
Reinforced Composite ◽  
Buckling Behavior

The buckling behavior of functionally graded carbon nanotube reinforced composite conical shells (FG-CNTRC-CSs) is here investigated by means of the first order shear deformation theory (FSDT), under a combined axial/lateral or axial/hydrostatic loading condition. Two types of CNTRC-CSs are considered herein, namely, a uniform distribution or a functionally graded (FG) distribution of reinforcement, with a linear variation of the mechanical properties throughout the thickness. The basic equations of the problem are here derived and solved in a closed form, using the Galerkin procedure, to determine the critical combined loading for the selected structure. First, we check for the reliability of the proposed formulation and the accuracy of results with respect to the available literature. It follows a systematic investigation aimed at checking the sensitivity of the structural response to the geometry, the proportional loading parameter, the type of distribution, and volume fraction of CNTs.

Concurrent Engineering Design of Sheet Stamping by Using an Inverse FE Approach

1997 ◽  
Author(s):  
Shiyong Yang ◽  
Kikuo Nezu
Keyword(s):  
Finite Element ◽  
Concurrent Engineering ◽  
Process Simulation ◽  
Three Dimensional ◽  
Sheet Forming ◽  
Design Stage ◽  
Forming Process ◽  
Element Analysis ◽  
Preliminary Design Stage ◽  
Product And Process

Abstract An inverse finite element (FE) algorithm is proposed for sheet forming process simulation. With the inverse finite element analysis (FEA) program developed, a new method for concurrent engineering (CE) design for sheet metal forming product and process is proposed. After the product geometry is defined by using parametric patches, the input models for process simulation can be created without the necessity to define the initial blank and the geometry of tools, thus simplifying the design process and facilitating the designer to look into the formability and quality of the product being designed at preliminary design stage. With resort to a commercially available software, P3/PATRAN, arbitrarily three-dimensional product can be designed for manufacturability for sheet forming process by following the procedures given.

An Area Preserving Transformation Algorithm for Press Forming Blank Development

1993 ◽  
Author(s):  
Nirmal K. Nair ◽  
James H. Oliver
Keyword(s):  
Time Complexity ◽  
Linear Time ◽  
Geometric Interpretation ◽  
Surface Geometry ◽  
Forming Process ◽  
Surface Design ◽  
Design Assessment ◽  
Press Forming ◽  
Blank Shape ◽  
Area Preserving

Abstract An efficient algorithm is presented to determine the blank shape necessary to manufacture a surface by press forming. The technique is independent of material properties and instead uses surface geometry and an area conservation constraint to generate a geometrically feasible blank shape. The algorithm is formulated as an approximate geometric interpretation of the reversal of the forming process. The primary applications for this technique are in preliminary surface design, assessment of manufacturability, and location of binder wrap. Since the algorithm exhibits linear time complexity, it is amenable to implementation as an interactive design aid. The algorithm is applied to two example surfaces and the results are discussed.

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