Truss Design and Optimization Using Stress Analysis and NURBS Curves

2018 ◽  
Author(s):  
Antonio Caputi ◽  
Miri Weiss Cohen ◽  
Caterina Rizzi ◽  
Davide Russo
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Elastic Energy ◽  
Solid Material ◽  
Parametric Representation ◽  
Optimization Method ◽  
Design And Optimization ◽  
Spline Curves ◽  
Topology And Shape Optimization ◽  
Gradient Based

This paper presents a novel design methodology, which combines topology and shape optimization to define material distribution in the structural design of a truss. Firstly, in order to identify the best layout, the topology optimization process in the design domain is carried out by applying the BESO (Bidirectional Evolutionary Structural Optimization) method. In this approach, the low energy elements are eliminated from an initial mesh, and a new geometry is constructed. This new geometry consists of a set of elements with a higher elastic energy. This results in a new division of material providing different zones, some subjected to higher stress and others containing less elastic energy. Moreover, the elements of the final mesh are re-arranged and modified, considering the distribution of tension. This new arrangement is constructed by aligning and rotating the original mesh elements coherently to the principal directions. In the Shape Optimization stage, the resulting TO (Topology Optimization) geometry is refined. A process of replacing the tabular mesh is performed by rearranging the remaining elements. The vertices of the mesh are set as control polygon vertices and used as reference to define the NURBS (Non-Uniform Rational B-Spline) curves. This provides a parametric representation of the boundaries, outlining the high elastic energy zones. The final stage is the optimization of the continuous and analytically defined NURBS curve outlining the solid material domain. The Shape Optimization is carried out applying a gradient-based optimization method.

Non-Probabilistic Based Topology Optimization Under External Load Uncertainty With Eigenvalue-Superposition of Convex Models

2013 ◽  
Author(s):  
Xike Zhao ◽  
Hae Chang Gea ◽  
Wei Song
Keyword(s):  
Topology Optimization ◽  
External Load ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimization Method ◽  
Convex Model ◽  
Structure Response ◽  
Gradient Based ◽  
Bounded Convex ◽  
Topology Optimization Method

In this paper the Eigenvalue-Superposition of Convex Models (ESCM) based topology optimization method for solving topology optimization problems under external load uncertainties is presented. The load uncertainties are formulated using the non-probabilistic based unknown-but-bounded convex model. The sensitivities are derived and the problem is solved using gradient based algorithm. The proposed ESCM based method yields the material distribution which would optimize the worst structure response under the uncertain loads. Comparing to the deterministic based topology optimization formulation the ESCM based method provided more reasonable solutions when load uncertainties were involved. The simplicity, efficiency and versatility of the proposed ESCM based topology optimization method can be considered as a supplement to the sophisticated reliability based topology optimization methods.

Optimum Design of Tractor Clutch PTO Finger by Using Topology and Shape Optimization

2015 ◽  
Author(s):  
O. Dogan ◽  
F. Karpat ◽  
N. Kaya ◽  
C. Yuce ◽  
M. O. Genc ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Topology Optimization ◽  
Shape Optimization ◽  
Optimization Techniques ◽  
Design Parameters ◽  
Agricultural Activities ◽  
Element Analysis ◽  
Design Life ◽  
Topology And Shape Optimization

Tractors are one of the most important agricultural machinery in the world. They provide agricultural activities in challenging conditions by using various agricultural machineries which are added on them. Therefore, there has been a rising demand for tractor use for agricultural activities. During the power transmission, tractor clutches are exposed to high static and cyclic loading directly. Thus, most of clutch parts fail before completing their design life which is under 106 cycles. Especially, because of the high stress, there are a number of fractures and breakages are observed around the pin area of the finger mechanisms. Due to these reasons, it is necessary to re-design these fingers by using modern optimization techniques and finite element analysis. This paper presents an approach for analysis and re-designs process of tractor clutch PTO finger. Firstly, the original designs of the PTO fingers are analyzed by using finite element analysis. Static structural analyses are applied on these fingers by using ANSYS static structural module. The boundary conditions are determined according to the data from the axial fatigue test bench. Afterwards, the stress-life based fatigue analyses are performed with respect to Goodman criterion. It is seem that the original design of the PTO finger, failed before the design life. Hence, the PTO finger is completely re-designed by using topology and shape optimization methods. Topology optimization is used to find the optimum material distribution of the PTO fingers. Topology optimization is performed in solidThinking Inspire software. The precise dimensions of the PTO fingers are determined by using shape optimization and response surface methodology. Two different design parameters, which are finger thickness and height, are selected for design of experiment and 15 various cases are analyzed. By using DOE method three different equations are obtained which are maximum stresses, mass, and displacement depending on the selected design parameters. These equations are used in the optimization as objective and constraint equations in MATLAB. The results indicate that the proposed models predict the responses adequately within the limits of the parameters being used. The final dimensions of the fingers are determined after shape optimization. The new designs of the PTO fingers are re-analyzed in terms of static and fatigue analysis. The new design of the PTO finger passed the analysis successfully. As a result of the study, the finger mass is increased 7% but it is quite small. Maximum Equivalent Von-Misses stress reduction of 25.3% is achieved. Fatigue durability of the PTO finger is improved 53.2%. The rigidity is improved up to 27.9% compared to the initial design. The optimal results show that the developed method can be used to design a durable, low manufacturing cost and lightweight clutch parts.

scholarly journals Gradient-based topology optimization of soft dielectrics as tunable phononic crystals

2021 ◽  
Author(s):  
Atul Kumar Sharma ◽  
Gal Shmuel ◽  
Oded Amir
Keyword(s):  
Topology Optimization ◽  
Electric Fields ◽  
Computational Cost ◽  
Optimization Method ◽  
Phononic Crystals ◽  
Frequency Bands ◽  
Design Variables ◽  
Gradient Based ◽  
Soft Dielectrics ◽  
Design Freedom

Dielectric elastomers are active materials that undergo large deformations and change their instantaneous moduli when they are actuated by electric fields. By virtue of these features, composites made of soft dielectrics can filter waves across frequency bands that are electrostatically tunable. To date, to improve the performance of these adaptive phononic crystals, such as the width of these bands at the actuated state, metaheuristics-based topology optimization was used. However, the design freedom offered by this approach is limited because the number of function evaluations increases exponentially with the number of design variables. Here, we go beyond the limitations of this approach, by developing an efficient gradient-based topology optimization method. The numerical results of the method developed here demonstrate prohibited frequency bands that are indeed wider than those obtained from the previous metaheuristics-based method, while the computational cost to identify them is reduced by orders of magnitude.

A Density Gradient Approach to Topology Optimization Under Design-Dependent Boundary Loading

2018 ◽  
Author(s):  
Cunfu Wang ◽  
Xiaoping Qian
Keyword(s):  
Topology Optimization ◽  
Density Gradient ◽  
Optimization Method ◽  
Spatial Gradient ◽  
Computationally Efficient ◽  
Physical Density ◽  
Gradient Based ◽  
Design Dependent Loads ◽  
Previous Iteration ◽  
Gradient Approach

The paper proposes a density gradient based approach to topology optimization under design-dependent boundary loading. In the density-based topology optimization method, we impose the design dependent loads through spatial gradient of the density. We transform design-dependent boundary loads into a volume form through volume integral of density gradient. In many applications where loadings only need to be exerted on partial boundary, we introduce an auxiliary loading density to keep track of the loading boundary. During the optimization, the loading density is updated by tracking the changes of the physical density in the vicinity of the loading boundary at previous iteration. The proposed approach is easy to implement and computationally efficient. In addition, by adding more auxiliary density fields, the proposed approach is applicable to multiple design-dependent loads. To prevent the intersection of different loading boundaries, a Heaviside projection based integral constraint is developed. Both heat conduction problems under convection loading and elastic problems under hydrostatic pressure loading are presented to illustrate the effectiveness and efficiency of the method.

Buckling Topology Optimization of Laminated Multi-Material Composite Structures

2006 ◽  
Author(s):  
Erik Lund
Keyword(s):  
Topology Optimization ◽  
Composite Structures ◽  
Optimization Problems ◽  
Combinatorial Problem ◽  
Optimization Method ◽  
Load Factor ◽  
Material Optimization ◽  
Material Stiffness ◽  
Gradient Based ◽  
Material Composite

The design problem of maximizing the buckling load factor of laminated multi-material composite shell structures is investigated using the so-called Discrete Material Optimization (DMO) approach. The design optimization method is based on ideas from multi-phase topology optimization where the material stiffness is computed as a weighted sum of candidate materials, thus making it possible to solve discrete optimization problems using gradient based techniques and mathematical programming. The potential of the DMO method to solve the combinatorial problem of proper choice of material and fiber orientation simultaneously is illustrated for a multilayered plate example and a simplified shell model of a spar cap of a wind turbine blade.

scholarly journals On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization—Part II: Viscous Flows

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 106
Author(s):  
Farzad Mohebbi ◽  
Ben Evans ◽  
Mathieu Sellier
Keyword(s):  
Shape Optimization ◽  
Viscous Flows ◽  
Optimization Method ◽  
Step Length ◽  
Aerodynamic Shape Optimization ◽  
Ansys Fluent ◽  
Transonic Flows ◽  
Aerodynamic Shape ◽  
Design Variables ◽  
Gradient Based

This study presents an extension of a previous study (On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization) to viscous transonic flows. In this work, we showed that the same procedure to derive an explicit expression for an exact step length βexact in a gradient-based optimization method for inviscid transonic flows can be employed for viscous transonic flows. The extended numerical method was evaluated for the viscous flows over the transonic RAE 2822 airfoil at two common flow conditions in the transonic regime. To do so, the RAE 2822 airfoil was reconstructed by a Bezier curve of degree 16. The numerical solution of the transonic turbulent flow over the airfoil was performed using the solver ANSYS Fluent (using the Spalart–Allmaras turbulence model). Using the proposed step length, a gradient-based optimization method was employed to minimize the drag-to-lift ratio of the airfoil. The gradient of the objective function with respect to design variables was calculated by the finite-difference method. Efficiency and accuracy of the proposed method were investigated through two test cases.

scholarly journals Coupled topology and shape optimization using an embedding domain discretization method

2021 ◽  
Vol 64 (4) ◽  
pp. 2687-2707
Author(s):  
Gabriel Stankiewicz ◽  
Chaitanya Dev ◽  
Paul Steinmann
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Optimization Problem ◽  
Optimization Methods ◽  
Density Field ◽  
Discretization Method ◽  
Topological Features ◽  
Topology And Shape Optimization ◽  
Discretization Technique ◽  
Domain Discretization

AbstractDensity-based topology optimization and node-based shape optimization are often used sequentially to generate production-ready designs. In this work, we address the challenge to couple density-based topology optimization and node-based shape optimization into a single optimization problem by using an embedding domain discretization technique. In our approach, a variable shape is explicitly represented by the boundary of an embedded body. Furthermore, the embedding domain in form of a structured mesh allows us to introduce a variable, pseudo-density field. In this way, we attempt to bring the advantages of both topology and shape optimization methods together and to provide an efficient way to design fine-tuned structures without predefined topological features.

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