Isogeometric analysis for parameterized LSM-based structural topology optimization

In this paper, we present an accurate and efficient isogeometric topology optimization method that integrates the non-uniform rational B-splines based isogeometric analysis and the parameterized level set method for minimal compliance problems. The same NURBS basis functions are used to parameterize the level set function and evaluate the objective function, and therefore the design variables are associated with the control points. The coefficient matrix that parameterizes the level set function is set up by a collocation method that uses the Greville abscissae. The zero-level set boundary is obtained from the interpolation points corresponding to the vertices of the knot spans. Numerical examples demonstrate the validity and efficiency of the proposed method.

Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed elements

In this paper, an approach based on the fast point-in-polygon (PIP) algorithm and trimmed elements is proposed for isogeometric topology optimization (TO) with arbitrary geometric constraints. The isogeometric parameterized level-set-based TO method, which directly uses the non-uniform rational basis splines (NURBS) for both level set function (LSF) parameterization and objective function calculation, provides higher accuracy and efficiency than previous methods. The integration of trimmed elements is completed by the efficient quadrature rule that can design the quadrature points and weights for arbitrary geometric shape. Numerical examples demonstrate the efficiency and flexibility of the method.

Multiscale isogeometric topology optimization for lattice materials

This paper presents isogeometric topology optimization (ITO) for periodic lattice materials, where non-uniform rational B-spline (NURBS) basis functions of CAD models are directly used in the finite element analysis to improve computational accuracy and efficiency. Two TO schemes that use asymptotic homogenization (AH) for the calculation of the mechanical properties are proposed for lattice materials with uniform and graded relative density respectively. To accelerate ITO for graded lattice materials, the mechanical properties are expressed as a function of the relative density of the unit cell, a step that avoids their iterative calculations during ITO. Three benchmark examples are presented to validate the proposed scheme with results that show tangible advantages, such as reduced computational time and faster convergence, of ITO over conventional TO.

A new isogeometric topology optimization using moving morphable components based on R-functions and collocation schemes

This paper presents a new isogeometric topology optimization (TO) method based on moving morphable components (MMC), where the R-functions are used to represent the topology description functions (TDF) to overcome the C1 discontinuity problem of the overlapping regions of components. Three new ersatz material models based on uniform, Gauss and Greville abscissae collocation schemes are used to represent both the Young’s modulus of material and the density field based on the Heaviside values of collocation points. Three benchmark examples are tested to evaluate the proposed method, where the collocation schemes are compared as well as the difference between isogeometric analysis (IGA) and finite element method (FEM). The results show that the convergence rate using R-functions has been improved in a range of 17%–60% for different cases in both FEM and IGA frameworks, and the Greville collocation scheme outperforms the other two schemes in the MMC-based TO.  

Hip implant design with three-dimensional porous architecture of optimized graded density

Even in a well-functioning total hip replacement, significant peri-implant bone resorption can occur secondary to stress shielding. Stress shielding is caused by an undesired mismatch of elastic modulus between the stiffer implant and the adjacent bone tissue. To address this problem, we present here a microarchitected hip implant that consists of a three-dimensional graded lattice material with properties that are mechanically biocompatible with those of the femoral bone. Asymptotic homogenization is used to numerically determine the mechanical and fatigue properties of the implant, and a non-gradient scheme of topology optimization is used to find the optimized relative density distribution of the porous implant under multiple constraints dictated by implant micromotion, pore size, porosity, and minimum manufacturable thickness of the cell elements. Obtained for a 38-year-old patient femur, bone resorption is assessed for postoperative conditions. The numerical results suggest that bone loss for the optimized implant is only 42% of that of a fully solid implant, here taken as benchmark, and 79% of that of a porous implant with uniform density. The architected hip implant presented in this work shows clinical promise in reducing bone loss while preventing implant micromotion, thereby contributing to reduce the risk of periprosthetic fracture and the probability of revision surgery.