engineering design

optimizing to surpass the limits

the menu

optimizing

the claim
	The form of a structure is the most elemental constituent of a conceptual design solution. It is the form that is captured in the first quick hand sketches, before calculations and models.
	A key hypothesis of this work is that patterns exist between efficient structural forms and design requirements. The patterns relate to the number and type of design requirements, such as stiffness, strength, reliability and cost.
the methodology
	create or recognize efficient structural forms, recognize patterns in structural form, evaluate designs in terms of design requirements like strength and stiffness, and, to select which designs to exclude or include in the set of viable design options.
the approach
topology optimization problem
topology optimization output from ANSYS
image processing
image resizing (10X) using bilinear interpolation
binary conversion by thresholding grayscale values
Euclidean distance transform (grayscale brightness proportional to edge distance)
Laplacian operator is an approximation to the linear second derivative of brightness B in the directions x and y:
Laplacian operator applied to previous Figure
binary conversion by thresholding Laplacian results
combination using logical AND
conditional erosion morphology operator
dilation morphology operator
erosion morphology operator
conditional erosion reapplied to show 4-connected skeleton
skeleton thickened and combined with Euclidean distance to show width
node points superimposed on skeleton
node points connected with line segments
final results
node adjustments
member sizes derived from Euclidean distance transform
conclusions and outlook
	Reasoning about node locations and the types of joints represented by nodes is closely related to fabrication cost. Initially it could be assumed that all the joints carry moment, thus avoiding the issue of stability. For economical fabrication, it would be necessary to study the effects of moment releases, or pin-jointed connections.
	Stability could be evaluated in a number of different ways. The topology of the structure may be evaluated using pattern recognition techniques such as graph matching, and stability may be evaluated using a set of heuristics. The stiffness matrix for the structure may be formed to validate stability.
	Pattern recognition techniques could be used to mine a database of records containing truss topology along with associated fabrication costs.
	Finally, member sizes, node locations, node types (pin or fixed), and fabrication cost estimates could be combined into a multicriteria optimization procedure to help guide the selection of a truss layout for detailed design.
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sponsor:	EMPIRE DS
conceptual optimization using image processing

Michael Gedig
Optimization of structures is a mature field and great progress has been achieved. With our approach we deviate from the "follow-the-leader" methods, but look sideways what other fields of science have to offer.