Focusing on the structural optimization of auxetic materials using data-driven methods, a back-propagation neural network (BPNN) based design framework is developed for petal-shaped auxetics using isogeometric analysis. Adopting a NURBS-based parametric modelling scheme with a small number of design variables, the highly nonlinear relation between the input geometry variables and the effective material properties is obtained using BPNN-based fitting method, and demonstrated in this work to give high accuracy and efficiency. Such BPNN-based fitting functions also enable an easy analytical sensitivity analysis, in contrast to the generally complex procedures of typical shape and size sensitivity approaches.
This paper proposes a new high-efficiency isogeometric topology optimization (HITO), including three part:
multilevel mesh, multigrid conjugate gradient method (MGCG) and local-update strategy, which improves the
efficiency in three aspects: mesh scale reduction, solving acceleration and design variables reduction. Four
benchmark examples are used to evaluate proposed method, and the results show that the proposed HITO
successfully reduces 37%–93% computational time compared to the conventional isogeometric topology optimization (CITO) and obtains consistent optimization results, which demonstrates the high-efficiency of
the HITO. Furthermore, the efficiency improvement of the HITO will be more significant for the large-scale
This paper presents a hierarchical spline based isogeometric topology optimization using moving morphable components (HITO-MMC). In this work, the adaptive isogeometric analysis implemented by hierarchical B-spline is adopted to efficiently and accurately assess the structural performance. An ersatz material model is derived from the Gaussian points of the hierarchy computational mesh to relate the geometric design variables with the objective and constraint of TO. To determine the iterative steps performing local refinement and the elements to be locally refined, a mark strategy is put forward based on the relative error of objective function and the value of topological description function (TDF). The mathematic model of HITO-MMC is reformulated by mapping the global displacement vector into the local displacement vector of the active elements on each level of the hierarchy computational mesh. The proposed HITO-MMC approach has twofold merits: (a) the optimization can be started from a relative coarse computational mesh and the mesh is locally refined during the course of TO, which result into
a highly computational efficiency; (b) more accurate results are obtained due to the use of high continuous hierarchical basis functions and denser mesh on structural boundary. Besides, continuous refinement is more effective to generate the optimal design than fixed NURBS mesh, and hierarchical local refinement is superior to continuous global refinement. The effectiveness of the proposed HITO-MMC is validated by a series of 2D and 3D numerical benchmarks.
This paper presents a triple acceleration method (TAM) for the topology optimization (TO), which consists of three parts: multilevel mesh, initial-value-based preconditioned conjugate-gradient (PCG) method, and local-update strategy. The TAM accelerates TO in three aspects including reducing mesh scale, accelerating solving equations, and decreasing the number of updated elements. Three benchmark examples are presented to evaluate proposed method, and the result shows that the proposed TAM successfully reduces 35–80% computational time with faster convergence compared to the conventional TO while the consistent optimization results are obtained. Furthermore, the TAM is able to achieve a higher speedup for large-scale problems, especially for the 3D TOs, which demonstrates that the TAM is an effective method for accelerating large-scale TO problems.
Isogeometric analysis (IGA), an approach that integrates CAE into conventional
CAD design tools, has been used in structural optimization for 10 years, with plenty of excellent
research results. This paper provides a comprehensive review on isogeometric shape
and topology optimization, with a brief coverage of size optimization. For isogeometric
shape optimization, attention is focused on the parametrization methods, mesh updating
schemes and shape sensitivity analyses. Some interesting observations, e.g. the popularity
of using direct (differential) method for shape sensitivity analysis and the possibility of developing
a large scale, seamlessly integrated analysis-design platform, are discussed in the
framework of isogeometric shape optimization. For isogeometric topology optimization
(ITO), we discuss different types of ITOs, e.g. ITO using SIMP (Solid Isotropic Material
with Penalization) method, ITO using level set method, ITO using moving morphable
com-ponents (MMC), ITO with phase field model, etc., their technical details and
applications such as the spline filter, multi-resolution approach, multi-material problems
and stress con-strained problems. In addition to the review in the last 10 years, the current
developmental trend of isogeometric structural optimization is discussed.
One of the major goals of isogeometric analysis is direct design-to-analysis, i.e., using computer-aided design (CAD) files for analysis without the need for mesh generation. One of the primary obstacles to achieving this goal is CAD models are based on surfaces, and not volumes. The boundary element method (BEM) circumvents this difficulty by directly working with the surfaces. The standard basis functions in CAD are trimmed nonuniform rational B-spline (NURBS). NURBS patches are the tensor product of one-dimensional NURBS, making the construction of arbitrary surfaces difficult. Trimmed NURBS use curves to trim away regions of the patch to obtain the desired shape. By coupling trimmed NURBS with a nonsingular BEM, the formulation proposed here comes close achieving the goal of direct design to analysis. Example calculations demonstrate its efficiency and accuracy.