Isogeometric shape optimization for design dependent loads

2021 ◽  
pp. 1-13
Author(s):  
Arkaprabho Pal ◽  
Sourav Rakshit
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Minimum Weight ◽  
Control Point ◽  
Optimization Approach ◽  
Shape Sensitivity ◽  
Body Forces ◽  
Design Variables ◽  
Design Dependent Loads ◽  
Material Layout

Abstract This paper presents a new isogeometric formulation for shape optimization of structures subjected to design dependent loads. This work considers two types of design dependent loads, namely surface loads like pressure where the direction and/or magnitude of force changes with the variation of boundary shape, and body forces that depend on the material layout. These problems have been mostly solved by topology optimization methods which are prone to difficulties in determination of the loading surface for pressure loads and problems associated with non-monotonous behaviour of compliance and low density regions for body forces. This work uses an isogeometric shape optimization approach where the geometry is defined using NURBS and the control point coordinates and control weights of the boundary are chosen as design variables. This approach accommodates the design dependent loads easily, in addition to its other advantages like exact geometry representation, local control, fewer design variables, excellent shape sensitivity, efficient mesh refinement strategies, and smooth results that can be integrated with CAD. Two classes of optimization problems have been discussed, they are minimum compliance problems subject to volume constraint and minimum weight problems subjected to local stress constraints. These problems are solved using convex optimization programs. Hence, expressions for full sensitivities are derived which is new for structural shape optimization problems with design dependent loads. Some representative engineering examples are solved and compared with existing literature to demonstrate the application of the proposed method.

Isogeometric Shape Optimization for Design Dependent Loads

2021 ◽  
Author(s):  
Arkaprabho Pal ◽  
Sourav Rakshit
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Optimization Approach ◽  
Analytical Sensitivity ◽  
Control Points ◽  
Minimum Compliance ◽  
Design Variables ◽  
Minimum Compliance Optimization ◽  
Design Dependent Loads ◽  
2D And 3D

Abstract This paper presents an isogeometric shape optimization approach for a special class of problems in structural optimization known as design dependent load problems. Isogeometric method has been widely used for structural analysis and shape optimization for its advantages in modeling smooth surfaces, high accuracy, local control, and interfacing with CAD tools. Isogeometric method may be of special advantage for shape optimization problems with design dependent loads as the loads in such class of problems depend on the geometry of the designed surface. The method outlined in this paper is applicable to design dependent load problems where there is a pressure load acting on the boundary of the structure, the direction of the pressure being normal to the profile of the designed structure. In this work minimum compliance optimization subject to volume constraint is considered and isogeometric formulations based on NURBS are presented for such class of problems. The control points of the boundaries of the NURBS geometries are taken as the design variables in the optimization problems. Analytical sensitivity formulations are derived for design dependent load problems and compared with numerically derived sensitivities. A few representative 2D and 3D examples are solved and compared with existing literature to demonstrate the application of the proposed method.

Study on Vibration Reduction Design of Steel-Composite Material Hybrid Mounting for Ship Based on Material Selection Optimization

2013 ◽  
Vol 694-697 ◽  
pp. 415-424
Author(s):  
Wei Wang ◽  
Lu Yun Chen ◽  
Yu Fang Zhang
Keyword(s):  
Power Flow ◽  
Optimization Problems ◽  
Material Selection ◽  
Vibration Reduction ◽  
Optimization Method ◽  
Optimization Approach ◽  
Structural Dynamic ◽  
Level Difference ◽  
Design Variables ◽  
Steel Composite

The material selection optimization for vibration reduction design is studied present article. By introducing the stacking sequence hypothesis of metal material, taking into account the power flow level difference and vibration level difference parameter, the mechanical parameters of the material and plies number are defined as design variables, and the mathematical model of structural dynamic optimization based on material selection optimization approach is established. Finally, a naval hybrid steel-composite mounting structure for example, by introducing genetic algorithm, the optimization problems is solved. The numerical results show that the optimization method is effective and feasible.

scholarly journals A comparative evaluation of genetic and gradient-based algorithms applied to aerodynamic optimization

2008 ◽  
pp. 103-126
Author(s):  
David W. Zingg ◽  
Marian Nemec ◽  
Thomas H. Pulliam
Keyword(s):  
Genetic Algorithm ◽  
Shape Optimization ◽  
Comparative Evaluation ◽  
Pareto Front ◽  
Optimization Problems ◽  
Aerodynamic Optimization ◽  
Design Variables ◽  
Gradient Based ◽  
Degree Of Convergence ◽  
Multipoint Optimization

A genetic algorithm is compared with a gradient-based (adjoint) algorithm in the context of several aerodynamic shape optimization problems. The examples include singlepoint and multipoint optimization problems, as well as the computation of a Pareto front. The results demonstrate that both algorithms converge reliably to the same optimum. Depending on the nature of the problem, the number of design variables, and the degree of convergence, the genetic algorithm requires from 5 to 200 times as many function evaluations as the gradientbased algorithm.

Multilevel Hierarchical Decomposition: Identification Procedures for Edge of Design Space Feasibility

2006 ◽  
Author(s):  
Somanath Nagendra ◽  
Jeff Midgley ◽  
Joseph B. Staubach
Keyword(s):  
High Performance ◽  
Design Space ◽  
Optimization Problems ◽  
Functional Dependence ◽  
Minimum Weight ◽  
Design Feature ◽  
Turbine Disk ◽  
System Level ◽  
Optimum Shape ◽  
Design Variables

In high performance machines, multiple active MDO constraints dictate the edge of feasibility, i.e. boundary of the design space. It is essential to have an accurate description of the boundary in terms of design variables. Given a sample of data, the recognition of a design feature (e.g. design shape) is not usually familiar to the design domain experts but must be extracted based on data-driven procedures. The “edge of feasibility” could be evaluated as a continuous or piece wise continuous function of active constraints. In this work, the focus is on a class of quasiseparable optimization problems. The subsystems for these problems involve local design shape variables and global system variables, but no variables from other subsystems. The system in this particular case is the engine component (i.e. HPT) and the subsystem is the turbine disk. The system is hierarchically decomposed to the system and subsystem components respectively. The HPT flowpath and its defined thermodynamic and geometric parameters define the system. The subsystem is the HPT turbine disk and its associated geometric shape variables. A system level DOE determines the design space of the HPT system. The optimized subsystem turbine disk is the solution to the DOE of the system and feasible disk designs are the shapes that can withstand the design loads and stresses. The focus of the paper is to develop a methodology that would systematically utilize minimum weight optimum shape designs across the design space and predict new designs close to being optimal in performance for a specified range of design conditions. The shape of minimum weight disks are identified as a solution of a system of inverse response surface equations that can determine disk shapes with good confidence. The methodology is developed using synthetic turbine disk problems with known regions of feasibility and infeasibility. The edge of feasibility is determined and the functional dependence on the design variables estimated.

An Algorithm for Automated Design Variable Selection in Structural Shape Optimization With Intrinsically Defined Geometry

1995 ◽  
Author(s):  
James M. Widmann ◽  
Sheri D. Sheppard
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Analysis Model ◽  
Structural Shape ◽  
Structural Shape Optimization ◽  
Design Variables ◽  
Sufficient Set ◽  
Compatibility Constraint ◽  
Selection Of

Abstract A major difficulty encountered in the shape optimization of structural components is the selection of an adequate set of shape design variables. The quality of the solution and the value of the optimal objective function depend on the chosen set of design variables. This paper presents an algorithm for the automated selection of intrinsically defined design variables to solve two-dimensional structural shape optimization problems. The algorithm arrives at a sufficient set of design variables by solving a series of optimization problems. Using the results of intermediate solutions, the algorithm adaptively refines the set of design variables until the solution converges. The algorithm specifies the addition and deletion of design variables and makes use of a model compatibility constraint to determine whether the analysis model must be updated. Two examples are presented which illustrate the effectiveness of the algorithm.

Intrinsic Geometry for Shape Optimal Design With Analysis Model Compatibility

1994 ◽  
Author(s):  
James M. Widmann ◽  
Sheri D. Sheppard
Keyword(s):  
Shape Optimization ◽  
Geometric Modeling ◽  
Explicit Knowledge ◽  
Optimization Problems ◽  
Structural Response ◽  
Analysis Model ◽  
Intrinsic Geometry ◽  
Structural Shape ◽  
Structural Shape Optimization ◽  
Design Variables

Abstract This paper presents a comparison of geometric modeling techniques and their applicability to structural shape optimization. A method of shape definition based on intrinsic geometric quantities is then outlined. Explicit knowledge of curvature and arc length allow for a quantitative assessment of the compatibility of analysis model with the design model when using finite elements to determine structural response quantities. The compatibility condition is formalized by controlling finite element idealization error and is incorporated into the shape optimization model as simple bounds on the curvature design variables. Several examples of shape optimization problems are solved using sequential quadratic programming which proves to be an effective tool for maintaining the geometric equality constraints that arise from intrinsically defined curves.

Multiple Objective Preform Die Shape Optimization Design for Controlling Forging’s Shape and Deforming Force during Forging Process

2011 ◽  
Vol 306-307 ◽  
pp. 1504-1507 ◽  
Author(s):  
Xin Hai Zhao ◽  
Guo Qun Zhao ◽  
Xiao Hui Huang ◽  
Yi Guo Luan
Keyword(s):  
Shape Optimization ◽  
Objective Function ◽  
Optimization Design ◽  
Control Point ◽  
Optimization Procedure ◽  
Multiple Objective ◽  
Forging Process ◽  
Weighted Sum Method ◽  
Design Variables ◽  
The Cost

In order to decrease the cost of the material and energy during the forging process, multiple preform die shape optimization design was carried out in this paper. Based on the FEM, a sensitivity analysis method was used to perform the optimization procedure. The shape of the forging and deforming force of the final forging was used to express the cost of material and energy respectively. Using the weighted sum method, the total objective function was gotton. The coordinates of the control point of the B-spline used to represent the preform die shape was determined as the optimization design variable. The sensitivity equations of the total objective function with respect to the design variables was developed. The multiple objective perform design optimization software was developed by FORTRAN language. And then, the preform die shape of an H-shaped forging process is optimized. The total objective function, sub-objective function, the shape of the preform die and the final forging during the optimization were given. After the optimiztion, a near net shape forging was obtained. At the same time, the deforming force decreased. The optimization results are very satisfactory.

Particle Swarm Methodologies for Engineering Design Optimization

2009 ◽  
Author(s):  
Singiresu S. Rao ◽  
Kiran K. Annamdas
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Multiple Objective ◽  
Optimization Approach ◽  
Objective Functions ◽  
Mixed Design ◽  
Swarm Optimization ◽  
Design Variables ◽  
Mixed Design Variables

Particle swarm methodologies are presented for the solution of constrained mechanical and structural system optimization problems involving single or multiple objective functions with continuous or mixed design variables. The particle swarm optimization presented is a modified particle swarm optimization approach, with better computational efficiency and solution accuracy, is based on the use of dynamic maximum velocity function and bounce method. The constraints of the optimization problem are handled using a dynamic penalty function approach. To handle the discrete design variables, the closest discrete approach is used. Multiple objective functions are handled using a modified cooperative game theory approach. The applicability and computational efficiency of the proposed particle swarm optimization approach are demonstrated through illustrate examples involving single and multiple objectives as well as continuous and mixed design variables. The present methodology is expected to be useful for the solution of a variety of practical engineering design optimization problems.

Fuzzy Optimization of Complex Systems Using Approximation Concepts

1997 ◽  
Vol 50 (11S) ◽  
pp. S97-S104 ◽  
Author(s):  
Hector A. Jensen ◽  
Abdon E. Sepulveda
Keyword(s):  
Original Problem ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Optimization Techniques ◽  
System Response ◽  
Optimization Approach ◽  
Design Variables ◽  
Intermediate Response ◽  
Intermediate Variables ◽  
Approximation Concepts

This paper presents a methodology for the efficient solution of fuzzy optimization problems. Design variables, as well as system parameters are modeled as fuzzy numbers characterized by membership functions. An optimization approach based on approximation concepts is introduced. High quality approximations for system response functions are constructed using the concepts of intermediate response quantities and intermediate variables. These approximations are used to replace the solution of the original problem by a sequence of approximate problems. Optimization techniques for non-differentiable problems which arise in fuzzy optimization are used to solve the approximate optimization problems. Example problems are presented to illustrate the ideas set forth.

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