Topology Optimization Under Independent Multi-Load With Uncertainty

2016 ◽  
Author(s):  
Hae Chang Gea ◽  
Xing Liu ◽  
Euihark Lee ◽  
Limei Xu
Keyword(s):  
Topology Optimization ◽  
Optimization Problem ◽  
Optimization Method ◽  
Engineering Practice ◽  
Worst Case ◽  
Load Uncertainty ◽  
Topology Optimization Problem ◽  
Level Problem ◽  
Upper Level ◽  
Mean Compliance

In this paper, topology optimization under multiple independent loadings with uncertainty is presented. In engineering practice, load uncertainty can be found in many applications. From the literature, researchers have focused mainly on problems containing only a single uncertain external load. However, such idealistic problems may not be very useful in engineering practice. Problems involving multi-loadings with uncertainty are more commonly found in engineering applications. This paper presents a method to solve a system which contains multiple independent loadings with load uncertainty. First, a two-level optimization problem is formulated. The upper level problem is a typical topology optimization problem to minimize the mean compliance in the design using the worst case conditions. The lower level optimization problem is to solve for the worst loadings corresponding to the critical structure response. At the lower level formulation, an unknown-but-bounded model is used to define uncertain loadings. There are two challenges in finding the worst loading case: non-convexity and multi-loadings. The non-convexity problem is addressed by reformulating the problem as an inhomogeneous eigenvalue problem by applying the KKT optimality conditions and the multi-uncertain loadings problem is solved by an iterative method. After the worst loadings are generated, the upper level problem can be solved by a general topology optimization method. The effectiveness of the proposed method is demonstrated by numerical examples.

Topology Optimization With Unknown-but-Bounded Load Uncertainty

2014 ◽  
Author(s):  
Xike Zhao ◽  
Wei Song ◽  
Hae Chang Gea ◽  
Limei Xu
Keyword(s):  
Topology Optimization ◽  
Strain Energy ◽  
Optimization Problem ◽  
Solution Procedure ◽  
Convex Model ◽  
Load Uncertainty ◽  
Topology Optimization Problem ◽  
Structure Response ◽  
Gradient Based ◽  
Upper Level

In this paper, convex modeling based topology optimization with load uncertainty is presented. The load uncertainty is described using the non-probabilistic based unknown-but-bounded convex model, and the strain energy based topology optimization problem under uncertain loads is formulated. Unlike the conventional deterministic topology optimization problem, the maximum possible strain energy under uncertain loads is selected as the new objective in order to achieve a safe solution. Instead of obtaining approximated solutions as used before, an exact solution procedure is presented. The problem is first formulated as a single level optimization problem, and then rewritten as a two-level optimization problem. The upper level optimization problem is solved as a deterministic topology optimization with the load which generated from the worst structure response in the lower level problem. The lower level optimization problem is to identify this worst structure response, and it is found equivalent to an inhomogeneous eigenvalue problem. Three different cases are discussed for accurately evaluating the global optima of the lower level optimization problem, while the corresponding sensitivities are derived individually. With the function value and sensitivity information ready, the upper level optimization problem can be solved through existing gradient based optimization algorithms. The effectiveness of the proposed convex modeling based topology optimization is demonstrated through different numerical examples.

Topology Optimization With Load Uncertainty as an Inhomogeneous Eigenvalue Problem

2015 ◽  
Author(s):  
Wei Song ◽  
Euihark Lee ◽  
Hae Chang Gea ◽  
Limei Xu
Keyword(s):  
Topology Optimization ◽  
Eigenvalue Problem ◽  
Optimization Problem ◽  
External Loading ◽  
Worst Case ◽  
Load Uncertainty ◽  
Critical Loading ◽  
Structure Response ◽  
Gradient Based ◽  
Upper Level

In this paper, a non-probabilistic based topology optimization method under an external load uncertainty is presented. In traditional topology optimization problems, external loadings that apply to structures are always assumed as deterministic, but an external loading with uncertainties is very common in many practical engineering applications. In this paper, load uncertainty is described as an unknown-but-bounded model and the maximum possible strain energy based topology optimization formulation under an uncertain load is solved for the worst case condition. This optimization problem can be rewritten as a two-level optimization problem: the upper level optimization problem is a deterministic topology optimization under a critical loading of the worst structure response, and the lower level optimization problem is to determine the critical loading corresponding to the worst structure response. The challenge of the lower level optimization problem is on its non-convexity which makes many gradient based search methods ineffective. To overcome this issue, the lower level optimization problem is reformulated based on the KKT optimality conditions as an inhomogeneous eigenvalue problem and is solved for the critical loading corresponding to the worst structure response. After the worst loading case is identified, the upper level problem can be solved through the existing gradient based optimization algorithms. The effectiveness of the proposed topology optimization under unknown-but-bounded external loading uncertainty is demonstrated through a few numerical examples.

Spot Weld/Adhesive Pattern Optimization

1996 ◽  
Author(s):  
R. J. Yang ◽  
Y. Rui ◽  
A. Mohammed ◽  
G. Singh
Keyword(s):  
Topology Optimization ◽  
Design Methodology ◽  
Optimization Problem ◽  
Optimization Method ◽  
Spot Weld ◽  
Linear Programming Method ◽  
Topology Optimization Problem ◽  
Maximum Stiffness ◽  
Stiffness Design ◽  
Topology Optimization Method

Abstract This research presents a new application of topology optimization. Patterns for spot weld location and adhesive distribution when joining body panels are determined by using the topology optimization method. The density method which parameterizes the density of each finite element is employed and a sequential linear programming method is used for solving the topology optimization problem. In this study, a B-Pillar to Rail Joint exemplifies the design methodology. The results show that patterns for optimal spot weld location and adhesive distribution can be obtained for a maximum stiffness design with mass constraints.

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.

Topology Optimization for the Single Phase Flow Using Two Point Flux Approximation Model

2013 ◽  
Author(s):  
Guang Dong ◽  
Yulan Song
Keyword(s):  
Porous Media ◽  
Topology Optimization ◽  
Optimization Problem ◽  
Single Phase ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Approximation Model ◽  
Single Phase Flow ◽  
Topology Optimization Problem ◽  
Flux Approximation

The topology optimization method is extended to solve a single phase flow in porous media optimization problem based on the Two Point Flux Approximation model. In particular, this paper discusses both strong form and matrix form equations for the flow in porous media. The design variables and design objective are well defined for this topology optimization problem, which is based on the Solid Isotropic Material with Penalization approach. The optimization problem is solved by the Generalized Sequential Approximate Optimization algorithm iteratively. To show the effectiveness of the topology optimization in solving the single phase flow in porous media, the examples of two-dimensional grid cell TPFA model with impermeable regions as constrains are presented in the numerical example section.

Multi-Objective Robust Optimization Under Interval Uncertainty Using Online Approximation and Constraint Cuts

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
W. Hu ◽  
M. Li ◽  
S. Azarm ◽  
A. Almansoori
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Computational Effort ◽  
Interval Uncertainty ◽  
Test Results ◽  
Robust Solution ◽  
Multi Objective ◽  
Function Calls ◽  
Level Problem ◽  
Upper Level

Many engineering optimization problems are multi-objective, constrained and have uncertainty in their inputs. For such problems it is desirable to obtain solutions that are multi-objectively optimum and robust. A robust solution is one that as a result of input uncertainty has variations in its objective and constraint functions which are within an acceptable range. This paper presents a new approximation-assisted MORO (AA-MORO) technique with interval uncertainty. The technique is a significant improvement, in terms of computational effort, over previously reported MORO techniques. AA-MORO includes an upper-level problem that solves a multi-objective optimization problem whose feasible domain is iteratively restricted by constraint cuts determined by a lower-level optimization problem. AA-MORO also includes an online approximation wherein optimal solutions from the upper- and lower-level optimization problems are used to iteratively improve an approximation to the objective and constraint functions. Several examples are used to test the proposed technique. The test results show that the proposed AA-MORO reasonably approximates solutions obtained from previous MORO approaches while its computational effort, in terms of the number of function calls, is significantly reduced compared to the previous approaches.

Optimal Viscous Damper Placement Using Level Set Topology Optimization Method

2010 ◽  
Author(s):  
Masoud Ansari ◽  
Amir Khajepour ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Discrete Optimization ◽  
Optimization Problem ◽  
Minimum Energy ◽  
Optimization Method ◽  
Discrete Optimization Problem ◽  
Placement Problem ◽  
New Approach ◽  
Optimal Damping

Vibration control has always been of great interest for many researchers in different fields, especially mechanical and civil engineering. One of the key elements in control of vibration is damper. One way of optimally suppressing unwanted vibrations is to find the best locations of the dampers in the structure, such that the highest dampening effect is achieved. This paper proposes a new approach that turns the conventional discrete optimization problem of optimal damper placement to a continuous topology optimization. In fact, instead of considering a few dampers and run the discrete optimization problem to find their best locations, the whole structure is considered to be connected to infinite numbers of dampers and level set topology optimization will be performed to determine the optimal damping set, while certain number of dampers are used, and the minimum energy for the system is achieved. This method has a few major advantages over the conventional methods, and can handle damper placement problem for complicated structures (systems) more accurately. The results, obtained in this research are very promising and show the capability of this method in finding the best damper location is structures.

Multi-material topology optimization of compliant mechanisms via solid isotropic material with penalization approach and alternating active phase algorithm

2020 ◽  
Vol 234 (13) ◽  
pp. 2631-2642
Author(s):  
Behzad Majdi ◽  
Arash Reza
Keyword(s):  
Topology Optimization ◽  
Isotropic Material ◽  
Close Agreement ◽  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Active Phase ◽  
Maximum Displacement ◽  
Topology Optimization Problem ◽  
Solid Phases ◽  
Ansys Workbench

The present study aims at providing a topology optimization of multi-material compliant mechanisms using solid isotropic material with penalization (SIMP) approach. In this respect, three multi-material gripper, invertor, and cruncher compliant mechanisms are considered that consist of three solid phases, including polyamide, polyethylene terephthalate, and polypropylene. The alternating active-phase algorithm is employed to find the distribution of the materials in the mechanism. In this case, the multiphase topology optimization problem is divided into a series of binary phase topology optimization sub-problems to be solved partially in a sequential manner. Finally, the maximum displacement of the multi-material compliant mechanisms was validated against the results obtained from the finite element simulations by the ANSYS Workbench software, and a close agreement between the results was observed. The results reveal the capability of the SIMP method to accurately conduct the topology optimization of multi-material compliant mechanisms.

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