Pascal Gadoury to present on November 30th

Pascal Gadoury will be presenting the work of his MASc thesis and also as part of the Material Seminar Series.  The title of Pascal’s talk is “Automated Optimization of Composite Material and Part Design”.  The abstract of his talk is below.  All are invited to attend.

Location: SITE B0138

TIME: 3:00pm (note this is in keeping with the starting time for Material Seminars).


Fibre reinforced composites are well suited for applications such as transportation and sporting goods, where light weight and high structural properties are required. These materials can offer superior specific strength and stiffness as well as better corrosion resistance than traditional metal alloys. Furthermore, they provide longer fatigue lives, tailorable properties and the ability to form to complex shapes. Given that these materials are orthotropic, the problem of selecting fibre alignments to maximize a part’s stiffness and strength is not trivial.

To this end, software  was developed that aims at facilitating the design of fibre-reinforced parts. This software combines a finite element analysis solver and a library of nonlinear optimization routines to minimize the deflection of a given part subjected to a given load.

The finite element solver which was developed first discretizes the selected part geometry through the use of the ‘tetgen’ tetrahedral mesh generator. This library generates exact constrained Delaunay tetrahedralizations given a set of boundary facets. These facets can be inputted through STL or PLY files, which can, in turn, be created with common solid modeling programs such as Solidworks.

Reduced generalized node tetrahedral elements were employed for modelling the response of each tetrahedral element to rotations and displacements at its nodes. An orthotropic material property stiffness matrix was formulated, along with a transformation matrix to account for the off-axis orientations of the fibres within each element. Specifically, each element’s properties were calculated as functions of the fibre volume fraction and alignment assigned to the element. The elements’ stiffness matrices were assembled to model the response of the entire part to the loading at its nodes. The Eigen linear algebra library was used for solving this assembled stiffness matrix.

Fibre volume fractions and orientations were initialized to an arbitrary starting value, and then dictated by a nonlinear optimization routine provided by the NLopt library. The optimization algorithm then used the displacement values and gradients calculated with the finite element analysis solver developed to hone in on orientations and volume fractions for each tetrahedral element, optimizing the stiffness of the given part.

Test parts consisting of a basic bar geometry, as well as more complex geometries were inputted to ascertain the performance and accuracy of the program.

Given sufficient time and computing power, this method could be used for optimizing more complex parts. With the addition of accurate failure criteria and density calculations, complex structures could automatically be generated which maximize specific strength instead.

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