Design of stiffened panels for stress and buckling via topology optimization

This paper investigates the weight minimization of stiffened panels simultaneously optimizing sizing, layout, and topology under stress and buckling constraints. An effective topology optimization parameterization is presented using multiple level-set functions. Plate elements are employed to model the stiffened panels. The stiffeners are parametrized by implicit level-set functions. The internal topologies of the stiffeners are optimized as well as their layout. A free-form mesh deformation approach is improved to adjust the finite element mesh. Sizing optimization is also included. The thicknesses of the skin and stiffeners are optimized. Bending, shear, and membrane stresses are evaluated at the bottom, middle, and top surfaces of the elements. A p-norm function is used to aggregate these stresses in a single constraint. To solve the optimization problem, a semi-analytical sensitivity analysis is performed, and the optimization algorithm is outlined. Numerical investigations demonstrate and validate the proposed method.

A multiple level-set method for 3D inversion of magnetic data

We have developed a multiple level-set method for inverting magnetic data produced by weak induced magnetization only. The method is designed to deal with a specific class of 3D magnetic inverse problems in which the magnetic susceptibility is known and the objective of the inversion is to find the boundary or geometric shape of the causative bodies. We adopt the conceptual representation of the subsurface geologic structure by a set of magnetic bodies, each having a uniform magnetic susceptibility embedded in a nonmagnetic background. This representation enables us to reformulate the magnetic inverse problem into a domain inverse problem for those unknown domains defining the supports of the magnetic causative bodies. Because each body may take on a variety of shapes, and we may not know the number of bodies a priori either, we use multiple level-set functions to parameterize these domains so that the domain inverse problem can be further reduced to an optimization problem of multiple level-set functions. To efficiently compute gradients of the nonlinear functional arising from the multiple level-set formulation, we take advantage of the rapid decay of the magnetic kernels with distance to significantly speed up the matrix-vector multiplications in the minimization process. We apply the new method to the synthetic and field data sets and determine its effectiveness.

CRACK ANALYSIS IN ORTHOTROPIC MEDIA USING COMBINATION OF ISOGEOMETRIC ANALYSIS AND EXTENDED FINITE ELEMENT

The main contribution of this paper is to propose an IGA formulation to model stationary cracks within orthotropic media by combination of XFEM enrichment functions and level set functions. For modeling cracks in solution field crack face and crack tips are considered separately and the control points that are related to each part are enriched with different approaches. The control points related with the crack face are enriched using the Heaviside enrichment functions. Level set functions are used to distinguish the control points correspond to crack tips and crack face. Stress intensity factors are employed to compare the results of XIGA with other methods. Several numerical examples considering crack inclination angle and material orientation axis are solved to verify the XIGA formulation. The results fairly conform to available methods, however less DOFs are used in XIGA.