A Designer’s Approach for Optimizing an End-Loaded

Cantilever Beam while Achieving Structural and

Manufacturing Requirements

Timothy M. Demers

November 5, 2009

• A bit behind schedule– First Progress Report posted 11/5 (3 weeks late)– Second Progress Report will be posted NLT

11/13 (1 week late)

• Back on schedule– Final Draft on 11/27– Final Report on 12/11

Schedule

Reason for Schedule Slip

Background• Optimization can be employed to find the best solution to problems that are quantifiable.

Determines optimum solution by calculating minimum or maximum value of a quantified parameter by varying design variables under the given design constraints.

• Structural optimization problems grouped into three categories:– Sizing optimization typically applied to truss-type structure. Plate thickness and beam cross-

sectional areas are examples of the sizing design variables which can be modified.– Shape optimization determines the optimal boundaries of a structure for a defined fixed topology.

Spline control points are adjusted.– Topology optimization overcomes a deficiency because the optimum topology is independent of

the initial starting design. For this reason topology optimization methods are commonly utilized at the conceptual stage of a design process.

• In many industries achieving an optimum design is beneficial and sometimes critical to success.

– Flight components - a lighter component and system can directly reduce launch costs and reduce the number of missions required.

• Optimization provides either the most efficient and effective use of the material in addition to minimizing the weight of the entire structure.

– In the studies examined by Fazil Sonmez, the goal of optimization “was to minimize the weight of the structure, in others to increase mechanical performance, e.g. to minimize stress concentration, maximize fracture strength, buckling strength, fatigue life, and heat flux, minimize peak contact stress, compliance, peak acceleration, and the probability of failure for brittle materials, and optimize dynamic behavior of structures”

Optimization Methods• Too many to list all

• Some are:– Trial and error– Most current techniques employ some form of

finite element analysis (FEA) software– Newer codes utilize fully stressed design

• ESO

Methodology• Based on evolutionary structural optimization

(ESO) method– Begin with simple, rectangular, two-dimensional,

cantilever beam with end load of 1500 pounds– Calculate beam thickness based on the highest stressed

section– Generate beam using Dassault Systems CATIA V5®– Analyze beam for baseline structural representation

using Comsol Multiphysics®– Design and analyze ten different beam designs to

eliminate the ineffective material– Compare and rank designs based on weight and strength– Iterate successful designs to create even lighter designs

or to resolve minor structural inadequacies– Compare and re-rank for final consideration