Key techniques and applications of adaptive growth method for stiffener layout design of plates and shells

Ding, Xuanming; Ji, Xuerong; Ma, Man; Hou, Jianyun

doi:10.3901/cjme.2013.06.1138

Cited by 4 publications

(4 citation statements)

References 19 publications

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“…Another method to design ribs is the so‐called adaptive growth technique. Stiffeners start from the seed points, grow and branch off towards direction with the maximal effectiveness of the global mechanical performance, which is dependent on the design sensitivity of the current structure [DJMH13, JDX14]. Chung and Lee [CL97] studied the optimal shapes and locations of ribs in order to increase the stiffness of structures using the topology optimization technique.…”

Section: Related Workmentioning

confidence: 99%

“…In engineering, most works focus on the analysis of rib‐shell structure, namely, analyze the mechanical property given the layout of ribs [PS01, ARR12]. Only a small number of works involve the location of ribs on some simple surfaces like plates, cylinders, etc [LS03, DJMH13]. And in computer graphics, researchers pay more attention to the generation and optimization of triangle‐based, quad‐based or hex‐dominant grid‐shell structures [LXW*11, CW07, LLW15].…”

Section: Introductionmentioning

confidence: 99%

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Rib‐reinforced Shell Structure

Zheng

You

et al. 2017

Computer Graphics Forum

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Figure 1: We present a computational framework to generate ribs to enhance the structural strength and stiffness of a shell (a). Our ribreinforced shell structure (c) costs the same amount of material as a pure shell without any ribs (a), while achieving much better mechanical performance. And (b) and (d) are coloring visualizations of the magnitude of von Mises stress of (a) and (c), respectively, under the same load and boundary conditions. Warmer color represents higher stress and red encodes stress exceeding the yield strength 42 MPa. The maximum stress in (b) is 109.84 MPa, which far exceeds 42 MPa, while the maximum stress in (d) is below 40 MPa with the contribution from ribs. The maximum stress of the shell is about 3 times of the stress of the rib-reinforced shell structure, indicating the latter achieves much higher strength than the former. We also fabricated the two structures by 3D printing and made a stiffness comparison as shown in Figure 19 which indicates much higher stiffness of the rib-reinforced shell structure. AbstractShell structures are extensively used in engineering due to their efficient load-carrying capacity relative to material volume. However, large-span shells require additional supporting structures to strengthen fragile regions. The problem of designing optimal stiffeners is therefore becoming a major challenge for shell applications. To address it, we propose a computational framework to design and optimize rib layout on arbitrary shell to improve the overall structural stiffness and mechanical performance. The essential of our method is to place ribs along the principal stress lines which reflect paths of material continuity and indicates trajectories of internal forces. Given a surface and user-specified external loads, we perform a Finite Element Analysis. Using the resulting principal stress field, we generate a quad-mesh whose edges align with this cross field. Then we extract an initial rib network from the quad-mesh. After simplifying rib network by removing ribs with little contribution, we perform a rib flow optimization which allows ribs to swing on surface to further adjust rib distribution. Finally, we optimize rib cross-section to maximally reduce material usage while achieving certain structural stiffness requirements. We demonstrate that our rib-reinforced shell structures achieve good static performances. And experimental results by 3D printed objects show the effectiveness of our method.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Rib‐reinforced Shell Structure

Zheng

You

et al. 2017

Computer Graphics Forum

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“…This design strategy is an effective way to solve the above problems by setting graded stiffening ribs with a variable stiffness. At present, most research focuses on transforming the layout design problem of stiffening ribs to find the optimal distribution of materials, including the variable thickness method [12,13], base structure method [14,15], adaptive growth method [16,17], etc. The essential idea of determining the optimal distribution of materials is similar to that of topology optimization.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Level Set Method for the Topology Optimization of Functionally Graded Structures

Shu

Gao

et al. 2022

Materials

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This paper presents a hybrid level set method (HLSM) to design novelty functionally graded structures (FGSs) with complex macroscopic graded patterns. The hybrid level set function (HLSF) is constructed to parametrically model the macro unit cells by introducing the affine concept of convex optimization theory. The global weight coefficients on macro unit cell nodes and the local weight coefficients within the macro unit cell are defined as master and slave design variables, respectively. The local design variables are interpolated by the global design variables to guarantee the C0 continuity of neighboring unit cells. A HLSM-based topology optimization model for the FGSs is established to maximize structural stiffness. The optimization model is solved by the optimality criteria (OC) algorithm. Two typical FGSs design problems are investigated, including thin-walled stiffened structures (TWSSs) and functionally graded cellular structures (FGCSs). In addition, additively manufactured FGCSs with different core layers are tested for bending performance. Numerical examples show that the HLSM is effective for designing FGSs like TWSSs and FGCSs. The bending tests prove that FGSs designed using HLSM are have a high performance.

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“…The boom is the key component of this structure and also the key bearing part of the work device [1]. The design of the boom has enormous influence on the working efficiency and service life [2].…”

Section: Introductionmentioning

confidence: 99%

Layout Topology Optimization for Inner Stiffeners of Excavator's Boom

Sheng

Liu

2014

AMR

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Aimed at the layout of inner stiffeners in excavator's boom, this paper puts forward an optimization method for the layout of box structure 's inner stiffeners and layout topology optimizes based on Evolutionary Structural Optimization (ESO). Analyzed the boom with the finite element method under the bucket digging condition, the results show that the inner stiffeners obtained by this method can improve the stress concentration phenomenon and the high stress distribution areas. The practices demonstrated the proposed method is effective and feasible.

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Key techniques and applications of adaptive growth method for stiffener layout design of plates and shells

Cited by 4 publications

References 19 publications

Rib‐reinforced Shell Structure

Rib‐reinforced Shell Structure

A Hybrid Level Set Method for the Topology Optimization of Functionally Graded Structures

Layout Topology Optimization for Inner Stiffeners of Excavator's Boom

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