Michell trusses study, rice u. nsf vigre group, summer 2013

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Michell trusses study, rice u. summer 2013- summary

1 Derived copy of michell trusses

1.1 Introduction

1.3 Existence of equilibrating trusses

1.4 Some economical trusses

1.5 Some global properties

1.6 Some local properties: cutting corners

1.7 Other deformations

2.1 Introduction

2.2 Michell spirals

2.3 Michell topology

2.4 Force equilibrium at a generic node

2.5 Linear propogation of forces

2.6 Michell topologies under a single bending load

2.7 Material volume of optimal structures

3 The steiner tree problem

3.1 Introduction

3.12 Definition

3.16 Definition

3.20 Definition

3.24 Computational complexity

3.25 The steiner ratio

3.26 Other applications

4 A look at a paper by strang and kohn

4.1 Introduction

4.2 Variational forms of the stress problems

4.3 The dual problems and optimality conditions

4.4 Open problems

5 Michell truss stress measure

5.1 Michelle trusses

5.2 Unidirectional curve stress

5.3 Stress in a truss

5.4 Cost of a truss

5.5 Cost minimization

6 Tensors, lagrange methods, and hausdorff measure

Source: OpenStax, Michell trusses study, rice u. nsf vigre group, summer 2013. OpenStax CNX. Sep 02, 2013 Download for free at http://cnx.org/content/col11567/1.2

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