Optimization Methods Applied to Selecting Support Positions in Fixture Design

1991 ◽  
Vol 113 (4) ◽  
pp. 412-418 ◽  
Author(s):  
R. J. Menassa ◽  
W. R. DeVries
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Objective Function ◽  
Design Problem ◽  
Optimization Methods ◽  
Design Criterion ◽  
Optimization Techniques ◽  
Fixture Design ◽  
The Finite Element Method ◽  
Numerical Examples

This paper proposes optimization techniques to assist in the design and evaluation of fixtures for holding prismatic workpieces. This formulation of the fixturing design problem takes into account deflection of the workpiece subjected to assembly or machining loads. Using the minimization of the workpiece deflection at selected points as the design criterion, the design problem is determining the positions of the fixture supports. The Finite Element Method is used for calculating deflections that are the basis for the design objective function, and the Broyden-Fletcher-Goldfarb-Shanno optimization algorithm is used to determine the fixture support positions. In this paper the proposed objective function is developed and the method is illustrated with three numerical examples.

scholarly journals Two Algorithms for a Class of Elliptic Problems in Shape Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Li Tian ◽  
Dai Xiaoxia ◽  
Zhang Chengwei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optimal Design ◽  
Shape Optimization ◽  
Variational Problem ◽  
Optimization Problem ◽  
Elliptic Boundary ◽  
The Finite Element Method ◽  
Numerical Examples ◽  
Elliptic Boundary Value

We propose two algorithms for elliptic boundary value problems in shape optimization. With the finite element method, the optimization problem is replaced by a discrete variational problem. We give rules and use them to decide which elements are to be reserved. Those rules are determined by the optimization; as a result, we get the optimal design in shape. Numerical examples are provided to show the effectiveness of our algorithms.

scholarly journals Optimal Synthesis of Flexible Link Mechanisms with Large Static Deflections

1975 ◽  
Vol 97 (2) ◽  
pp. 520-526 ◽  
Author(s):  
N. M. Sevak ◽  
C. W. McLarnan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Nonlinear Problems ◽  
Optimization Techniques ◽  
Large Deflections ◽  
The Finite Element Method ◽  
Flexible Link ◽  
Variable Metric ◽  
Function Generation ◽  
Variable Metric Method

Flexible link mechanisms (commonly referred to as flexural mechanisms) subjected to large static deflections are analyzed and synthesized for function generation. The large deflections present nonlinear problems. The nonlinear analysis is performed by the finite element method with aid of Martin’s linear incremental procedure and the synthesis problems are solved by the optimization techniques of Fletcher and Powell’s variable metric method. The techniques are demonstrated on mechanisms in which one or two links are flexible. The obtained analytical results are verified experimentally.

Dynamics of a 3D Micropolar Beam Model

2014 ◽  
Author(s):  
Soroosh Hassanpour ◽  
G. R. Heppler
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Equations ◽  
External Loading ◽  
Beam Model ◽  
The Finite Element Method ◽  
Numerical Examples ◽  
3D Space ◽  
Different Types ◽  
Modal Behavior

The development of a simplified micropolar beam model is presented and the governing dynamic equations for a micropolar beam deforming in 3D space, under different types of external loading and boundary conditions are derived. The dynamic equations are derived from Hamilton’s principle and the finite element method is used to provide numerical examples. The modal behavior of the developed micropolar beam model and the conditions under which the results of classical beam models will be recovered are presented.

Analysis of developable shells with special reference to the finite element method and circular cylinders

1976 ◽  
Vol 281 (1300) ◽  
pp. 113-170 ◽  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Variational Principle ◽  
Rigid Body ◽  
The Finite Element Method ◽  
Body Movements ◽  
Numerical Examples ◽  
Lines Of Curvature ◽  
Element Method

The paper begins by noting that the practical and efficient numerical analysis of thin walled shells is far from a reality. Groundwork for the investigation starts with an examination of existing sufficiency conditions for convergence of the finite element method of analysis with refinement of mesh size; new and more practical conditions are then given specifically for shells. Working formulae of a suitable first approximation theory for the linear small deflexion behaviour are then given for arbitrary shells in lines of curvature and in geodesic coordinates. A variational principle is introduced which is more general than that for the well known assumed stress hybrid finite element model; its purpose is to provide a means to overcome the excessive rank deficiency which is sometimes encountered in the derive element stiffness matrix. , The formulae are next specialized to general developable shells for they are tne simplest to analyse and frequently occur in technology. Emphasis is given to the derivation of general formulae governing inextensional deformation, membrane action and rigid body movement because these constitute important factors in any adequate numerical analysis. . . , Specific application is made to circular cylindrical shells by first considering the interpolation of the kinematic continuity conditions along an arbitrary geodesic line. Details and numerical examples are provided for the first known fully compatible lines of curvature rectangular finite element which directly recovers arbitrary rigid body movements as well as inextensional deformations and membrane actions. The paper concludes with details and numerical examples of an arbitrarily shaped triangular finite element which employs the above mentioned variational principle m conjunction with linearly varying stress fields. All the rigid body movements are directly recovered as well as inextensional deformations and membrane actions. It is anticipated that this finite element and its derivatives will find widespread application.

scholarly journals Numerical Solution of Some Differential Equations with Henstock–Kurzweil Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
D. A. León-Velasco ◽  
M. M. Morín-Castillo ◽  
J. J. Oliveros-Oliveros ◽  
T. Pérez-Becerra ◽  
J. A. Escamilla-Reyna
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Differential Equations ◽  
Numerical Solution ◽  
Elliptic Problem ◽  
The Finite Element Method ◽  
Weak Formulation ◽  
Numerical Examples ◽  
Integrable Functions ◽  
Bounded Variation Functions

In this work, the Finite Element Method is used for finding the numerical solution of an elliptic problem with Henstock–Kurzweil integrable functions. In particular, Henstock–Kurzweil high oscillatory functions were considered. The weak formulation of the problem leads to integrals that are calculated using some special quadratures. Definitions and theorems were used to guarantee the existence of the integrals that appear in the weak formulation. This allowed us to apply the above formulation for the type of slope bounded variation functions. Numerical examples were developed to illustrate the ideas presented in this article.

Swarm optimization of stiffeners locations in 2-D structures

2012 ◽  
Vol 60 (2) ◽  
pp. 241-246 ◽  
Author(s):  
M. Szczepanik ◽  
T. Burczyński
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
The Finite Element Method ◽  
Particle Swarm Optimizer ◽  
Effective Technique ◽  
Swarm Optimization ◽  
Numerical Examples ◽  
Computer Aided ◽  
Plates And Shells ◽  
Bending Plates

Abstract. The paper is devoted to the application of the swarm methods and the finite element method to optimization of the stiffeners location in the 2-D structures (plane stress, bending plates and shells). The structures are optimized for the stress and displacement criteria. The numerical examples demonstrate that the method based on the swarm computation is an effective technique for solving the computer aided optimal design. The additional comparisons of the effectiveness of the particle swarm optimizer (PSO) and evolutionary algorithms (EA) are presented.

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