• Dr. Sara Jabbarizadeh
  • American Bureau of Shipping
  • 1060 Torgersen Hall
  • 5:00 p.m.
  • Faculty Host: Dr. Leigh McCue-Weil

Compared to polynomial discretization, representing the geometry using Computer Aided Design (CAD)-based functions can potentially help avoid geometrical inaccuracies that are common in conventional computational analysis methods. This is mainly due to the fact that CAD-based analysis uses an exact representation of the geometry instead of an approximation by meshing which in turn, eliminates the need for a rigorous meshing process that is necessary in classic Finite Element Analysis. Despite the advantages of this method, which is generally referred to as Isogeometric Analysis since it employs a single basis function both for representing the geometry and estimating the solution, it has its own unique challenges that need to be meticulously studied. To this end, this seminar covers topics from a doctoral research conducted at the University of Michigan which aimed to compare non-linear analyses of two-dimensional curved membranes under different loading conditions using analytical and numerical methods.

The Developed methods were applied to curved membranes that were used to model the skirt system of Air Cushion Vehicles (ACVs) made of non-stretchable flexible rubber-like materials. In particular, an analytical method was developed based on equilibrium equations for a specific geometry which related the tension in the membrane to the deformed geometry. These equations were solved using the Newton-Raphson Method. Also a classic Finite Element Method (FEM) was developed using the “stiffness influence coefficient method”, where elements were represented by arcs, and displacements of nodes were selected as degrees of freedom. In another method, the geometry was described using a quadratic Bezier curve. The Principle of Virtual Work was then applied which allowed for nonlinear stress-strain relationship and the application of non-conservative loads. To solve for large deformations, equilibrium equations were established for the current state. All constraints were applied using the Lagrange Multiplier method. In addition to inextensible membranes, elastic membranes were also studied using bending and stretching strain energy. By comparing results obtained from these methods, it was concluded that arc-element FEM was an accurate method of good convergence rate when compared with the other method although it had limitations when treating curves with low curvature sections. While the Bezier-based analysis overcame these limitations, it introduced the uneven movements of control points that should be treated with design optimization and regularization.