Simultaneous Shape Optimization Research Articles

Simultaneous optimization of shape and topology for solid structure (Proposal of a topology optimization method with variable design domain)

Simultaneous optimization of shape and topology for solid structure (Proposal of a topology optimization method with variable design domain)

Fast-SNARF: A Fast Deformer for Articulated Neural Fields.

Neural fields have revolutionized the area of 3D reconstruction and novel view synthesis of rigid scenes. A key challenge in making such methods applicable to articulated objects, such as the human body, is to model the deformation of 3D locations between the rest pose (a canonical space) and the deformed space. We propose a new articulation module for neural fields, Fast-SNARF, which finds accurate correspondences between canonical space and posed space via iterative root finding. Fast-SNARF is a drop-in replacement in functionality to our previous work, SNARF, while significantly improving its computational efficiency. We contribute several algorithmic and implementation improvements over SNARF, yielding a speed-up of 150×. These improvements include voxel-based correspondence search, pre-computing the linear blend skinning function, and an efficient software implementation with CUDA kernels. Fast-SNARF enables efficient and simultaneous optimization of shape and skinning weights given deformed observations without correspondences (e.g. 3D meshes). Because learning of deformation maps is a crucial component in many 3D human avatar methods and since Fast-SNARF provides a computationally efficient solution, we believe that this work represents a significant step towards the practical creation of 3D virtual humans.

Optimizing the Shape and Chemical Ordering of Nanoalloys with Specialized Walkers

AbstractNew algorithms for the optimization of alloy nanoparticles (nanoalloys) are presented. The new algorithms are based on the concept of multiple basin‐hopping walkers running in parallel, each with its own specialized task—the flying walker, exploring the energy landscape at high temperatures to sample different geometric structures, and the landing and hiking walkers mainly refining the optimization of chemical ordering at low temperatures. These algorithms are referred to as flying‐landing (FL) and flying‐landing‐hiking (FLH). The algorithms are tested against several benchmarks (AuCu and AuRh clusters of 400 atoms and PtNi clusters of 38 and 55 atoms). In all cases, both FL and FLH are shown to perform very well compared to previous results in the literature. In addition, the algorithms are applied to the optimization of larger AgCu nanoparticles, with sizes up to 4000 atoms, in order to establish the behavior of the mixing energy and to compare full global optimization of shape and chemical ordering with optimization of chemical ordering alone at a fixed shape. In general, the results show that the simultaneous optimization of shape and chemical ordering is necessary in many cases, and that the FLH approach is especially efficient for that purpose.

Simultaneous optimization of shape and topology for stiffener creation

In this paper, we propose a method for designing stiffeners on thin plate structures by shape and topology optimization. The compliance is minimized under the constraints of volume and equilibrium equations. The optimal stiffeners’ shape and placement are simultaneously determined. Shape optimization and topology optimization are formulated as distributed-parameter optimization problem, in which the shape gradient function and density gradient function are derived by using the adjoint equations and the equilibrium equation. The shape optimization is performed by applying the shape gradient function to the H1 gradient method for vector variable, and the topology optimization is performed by applying the density gradient function to the H1 gradient method for scalar deign variable using the SIMP method. Several numerical examples are presented to confirm the effectiveness of the proposed method for the design of stiffeners.

Simultaneous optimization of material orientation angle and shape/topology of CFRP shell structure

The objective of this study is to develop a method for simultaneous optimization of shape, topology and orientation angle to maximize the stiffness of CFRP shell structures under volume constraints. In the optimization of orientation angle, the material directions of orthotropic anisotropic material in finite elements are used as design variable. The optimal shape is determined by the H1 gradient method for vector variables, and the optimal solutions for topology optimization and orientation angle are determined by the H1 gradient method for scalar variables. The effectiveness of the proposed method is confirmed through a numerical example.

Simultaneous shape and mesh quality optimization using pre-shape calculus

Abstract Computational meshes arising from shape optimization routines commonly suffer from decrease of mesh quality or even destruction of the mesh. In this work, we provide an approach to regularize general shape optimization problems to increase both shape and volume mesh quality. For this, we employ pre-shape calculus as established in Luft and Schulz (2021). Existence of regularized solutions is guaranteed. Further, consistency of modified pre-shape gradient systems is established. We present pre-shape gradient system modifications, which permit simultaneous shape optimization with mesh quality improvement. Optimal shapes to the original problem are left invariant under regularization. The computational burden of our approach is limited, since additional solution of possibly larger (non-)linear systems for regularized shape gradients is not necessary. We implement and compare pre-shape gradient regularization approaches for a 2D problem, which is prone to mesh degeneration. As our approach does not depend on the choice of metrics representing shape gradients, we employ and compare several different metrics.

Geometry and topology optimization of plane frames for compliance minimization using force density method for geometry model

A new method is proposed for simultaneous optimization of shape, topology and cross section of plane frames. Compliance against specified loads is minimized under constraint on structural volume. Difficulties caused by the melting nodes can be alleviated to some extent by introducing force density as design variables for defining the geometry, where the side constraints are assigned for force density to indirectly avoid the existence of extremely short members. Force density method is applied to an auxiliary cable-net model with different boundary and loading conditions so that the regularity of force density matrix is ensured by positive force densities. Sensitivity coefficients of the objective and constraint functions with respect to the design variables are also explicitly calculated. After the optimal geometry of the frame is obtained, the topology is further improved by removing the thin members and combining closely spaced nodes. It is demonstrated in the numerical examples of three types of frames that rational geometry and topology can be achieved using the proposed method, and the effect of bending moment on the optimal solution is also discussed.

Simultaneous optimization of shape and topology of free-form shells based on uniform parameterization model

In current optimization methods for free-form shells, the shape and topology are usually optimized separately. These methods are based on the assumption that the shape and topology of a shell influence each other only slightly, but this is not always correct. Moreover, different parameterization models are used in the shape optimization and topology optimization of free-form shells, which brings difficulties to carry out the integrated optimization. To solve this problem, an integrated method is proposed for simultaneously optimizing shape and topology for free-form shells. A uniform parameterization model based on NURBS solids is established to parameterize the free-form shells. In this model, only a small number of variables are used to describe both the shape and topology of the shell. In this way, the integrated optimization problem can be simplified, thus decrease the computational complexity. The integrated optimization of shape and topology is a complicated and large-scale optimization problem. Solving this problem requires a suitable optimization method. In this paper, the Method of Moving Asymptotes (MMA) is adopted. Finally, numerical examples are presented to address the importance of the optimization sequences and show the effectiveness and application of the proposed method.

Simultaneous optimization of shape, thickness and topology of shell structures using sigmoid function

Simultaneous optimization of shape, thickness and topology of shell structures using sigmoid function

Simultaneous optimization of shape, thickness and topology of shell structures using sigmoid function

Simultaneous optimization of shape, thickness and topology of shell structures using sigmoid function

Simultaneous optimization of Shape and Topology of laminated shell structures for minimizing multi-objective compliance

Simultaneous optimization of Shape and Topology of laminated shell structures for minimizing multi-objective compliance

A moving bounds strategy for the parameterization of geometric design variables in the simultaneous shape optimization of curved shell structures and openings

A moving bounds strategy is proposed to implement simultaneous shape optimization of curved shell structures and openings. Design variables related to the hole shape are constrained in a planar reference domain by the moving bounds whose values are adaptively updated as functions of design variables related to the surface by an arc-length rule. It is shown that this strategy is essential not only to ensure the geometric consistence in the simultaneous design process but also to hold the shape-preserving of the mapped FE mesh from reference domains. Numerical results are presented to validate the proposed method.

J0110105 形状と応力の同時最適化によるテンセグリティ構造の最小質量設計([J011-01]解析・設計の高度化・最適化(1))

J0110105 形状と応力の同時最適化によるテンセグリティ構造の最小質量設計([J011-01]解析・設計の高度化・最適化(1))

SIMULTANEOUS OPTIMIZATION OF SHAPE AND FLOW PARAMETERS FOR COMBINED FREE AND FORCED CONVECTION IN VERTICAL CHANNELS

Simultaneous optimization of shape and flow parameters is performed for a combined free and forced convection flow through vertical rectangular channels with moving walls. The laminar flow is assumed to be fully developed in the axial direction. The wall velocity, the axial pressure gradient and the channel height in the transverse plane are taken as the optimization parameters. The sensitivity expressions of both the objective function and the flow rate constraint of optimization are obtained in terms of the relevant physical variables, as well as adjoint variables which satisfy additional p.d.e.'s. All equations are discretized using the finite element method. Numerical results are provided for the present constrained optimization problem for various values of the problem parameters which include the moving wall segment size and the Rayleigh number. The results indicate that with increased Rayleigh number the optimal values of the wall velocity and the axial pressure gradient are increased, while the optimal value of the channel height is decreased. General sensitivity expressions are also presented in the appendix which might be utilized for arbitrary boundary variations along with arbitrary optimization objectives in other investigations. © 1997 by John Wiley & Sons, Ltd.

Simultaneous optimization of shape and laminate configurations of laminated panels under multiple loadings

The present paper shows an optimum design approach on laminated composite structures subjected to multiple in-plane loadings. A simplified design approach is developed to optimize layer angle and layer thickness distributions of composite structures, which leads to a simultaneous optimization of a structural shape and laminate configurations. An explicit optimal relation is derived for layer angles and layer thickness ratios in a single-element laminate, using the minimum strain energy criterion. Next, a strength optimization approach on a multi-element laminated panel under multiple loadings is developed for determining layer angle and layer thickness distributions. The present approach can determine a rough structural shape in addition to layer angle and layer thickness distributions. The optimal structure can be efficiently obtained with a small number of finite element analyses.

Approach to Problem of Vibration: Simultaneous Optimization of Shape and Topology.

This paper proposes a method for designing light and rigid structures that maximizes the natural frequency of the structure for a designated mode. A design variable `density' is introduced into the finite element method and is related to the material properties of a 3-dimensional solid element. Thus a structure is expressed as a density distribution inside its occupiable domain, and the optimal structure is obtained searching for the most suitable density distribution. The proposed method makes it possible to find the optimal shape and topology simultaneously. The dynamic characteristics of the structure are improved by repeatedly modifying its density distribution.

Simultaneous material/load/shape variations of thermoelastic structures

A continuous approach is adopted in order to find the total variation of a general performance criterion. The present analysis may find important physical applications in the simultaneous shape optimization and control of large space structures in time by applied thermal and/or mechanical loads. The adjoint variable method and the material derivative concept are used to find the sensitivity expressions

Shape optimization of satellite tanks for minimum weight and maximum storage capacity

The aim of structural design is to determine the dimensions and the shape of a system that fulfils certain requirements in an optimal way. Although this problem is not at all new, the application of mathematical algorithms together with multicriteria and shape optimization techniques as strategies for achieving an optimum are still very rarely used in practice. The efficiency of the optimization procedure SAPOP is demonstrated through the shape optimization of ultra light shell structures (e.g. satellite tanks) for which bending effects as well as the influence of large deformations in the shell theory are taken into account. After establishing a corresponding transfer matrix method for analysis, the meridional shape can be determined by using special shape functions (modified ellipsoids) and a “direct” shape optimization strategy. In addition, simultaneous optimization of shape and wall thickness distribution is introduced.