## Discrete Variables with a Two Bar Truss Design

## Main.DiscreteDesign History

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Attach:group50.png This assignment can be completed in groups of two. Additional guidelines on individual, collaborative, and group assignments are provided under the [[Main/CourseStandards | Expectations link]].

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[[Attach:discrete_twobar.pdf | Two Bar Truss Design with Discrete Variables]]

to:

* [[Attach:discrete_twobar.pdf | Two Bar Truss Design Problem with Discrete Variables]]

* [[Attach:discrete_twobar.zip | Two Bar Truss Files (MATLAB and Python)]]

* [[Attach:discrete_twobar.zip | Two Bar Truss Files (MATLAB and Python)]]

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!!!! Objective Function Plot

One part of the assignment asks you to select width and load as variables for a 3d optimal surface plot and plot the solution of the optimization problem to minimize deflection at each of the width / load combinations. This tutorial example shows how to do this same activity but for the alternative problem of minimizing weight.

* [[Attach:twobar_obj_plot.zip | Two Bar Objective Plot Files]]

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Attach:collaborative50.png This assignment can be completed in collaboration with others. Additional guidelines on individual, collaborative, and group assignments are provided under the [[Main/CourseStandards | Expectations link]].

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(:title Discrete Variables with a Two Bar Truss Design:)

(:keywords nonlinear, optimization, engineering optimization, two-bar optimization, engineering design, interior point, active set, differential, algebraic, modeling language, university course:)

(:description Engineering design of a two-bar structure to support a load. Discrete optimization principles are used to design the system.:)

We are revisiting the two-bar truss problem but with design variables allowed only at discrete values instead of continuous values. In many engineering design problems, the design variables are not continuous but are possible only at select levels known as βdiscreteβ values. These levels may be binary (e.g. 0 or 1), integer (e.g. 5, 6, 7, 8), or at real number values (e.g. 0.05, 0.10, 0.20, 0.50). Recall that we are interested in designing a truss that has a minimum weight, will not yield, will not buckle, and does not deflect "excessivelyβ.

[[Attach:discrete_twobar.pdf | Two Bar Truss Design with Discrete Variables]]

Attach:twobar250.png

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!!!! Objective Function Plot

One part of the assignment asks you to select width and load as variables for a 3d optimal surface plot and plot the solution of the optimization problem to minimize deflection at each of the width / load combinations. This tutorial example shows how to do this same activity but for the alternative problem of minimizing weight.

* [[Attach:twobar_obj_plot.zip | Two Bar Objective Plot Files]]

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<iframe width="560" height="315" src="https://www.youtube.com/embed/GB0NYz-k8ZM?rel=0" frameborder="0" allowfullscreen></iframe>

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Attach:collaborative50.png This assignment can be completed in collaboration with others. Additional guidelines on individual, collaborative, and group assignments are provided under the [[Main/CourseStandards | Expectations link]].

----

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(:keywords nonlinear, optimization, engineering optimization, two-bar optimization, engineering design, interior point, active set, differential, algebraic, modeling language, university course:)

(:description Engineering design of a two-bar structure to support a load. Discrete optimization principles are used to design the system.:)

We are revisiting the two-bar truss problem but with design variables allowed only at discrete values instead of continuous values. In many engineering design problems, the design variables are not continuous but are possible only at select levels known as βdiscreteβ values. These levels may be binary (e.g. 0 or 1), integer (e.g. 5, 6, 7, 8), or at real number values (e.g. 0.05, 0.10, 0.20, 0.50). Recall that we are interested in designing a truss that has a minimum weight, will not yield, will not buckle, and does not deflect "excessivelyβ.

[[Attach:discrete_twobar.pdf | Two Bar Truss Design with Discrete Variables]]

Attach:twobar250.png

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!!!! Objective Function Plot

One part of the assignment asks you to select width and load as variables for a 3d optimal surface plot and plot the solution of the optimization problem to minimize deflection at each of the width / load combinations. This tutorial example shows how to do this same activity but for the alternative problem of minimizing weight.

* [[Attach:twobar_obj_plot.zip | Two Bar Objective Plot Files]]

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<iframe width="560" height="315" src="https://www.youtube.com/embed/GB0NYz-k8ZM?rel=0" frameborder="0" allowfullscreen></iframe>

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Attach:collaborative50.png This assignment can be completed in collaboration with others. Additional guidelines on individual, collaborative, and group assignments are provided under the [[Main/CourseStandards | Expectations link]].

----

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