scholarly journals Adaptive thermodynamic topology optimization

2020 ◽  
Vol 63 (1) ◽  
pp. 95-119
Author(s):  
Andreas Vogel ◽  
Philipp Junker
Keyword(s):  
Topology Optimization ◽  
Degrees Of Freedom ◽  
Design Space ◽  
Memory Requirement ◽  
Adaptive Meshing ◽  
Adaptive Remeshing ◽  
Fine Structures

AbstractThe benefit of adaptive meshing strategies for a recently introduced thermodynamic topology optimization is presented. Employing an elementwise gradient penalization, stability is obtained and checkerboarding prevented while very fine structures can be resolved sharply using adaptive meshing at material-void interfaces. The usage of coarse elements and thereby smaller design space does not restrict the obtainable structures if a proper adaptive remeshing is considered during the optimization. Qualitatively equal structures and quantitatively the same stiffness as for uniform meshing are obtained with less degrees of freedom, memory requirement and overall optimization runtime. In addition, the adaptivity can be used to zoom into coarse global structures to better resolve details of interesting spots such as truss nodes.

scholarly journals A new stress-based topology optimization approach for finding flexible structures

2021 ◽  
Author(s):  
Martin Noack ◽  
Arnold Kühhorn ◽  
Markus Kober ◽  
Matthias Firl
Keyword(s):  
Topology Optimization ◽  
Stress State ◽  
Design Space ◽  
Flexible Structures ◽  
Optimization Approach ◽  
Principal Stresses ◽  
Output Displacement ◽  
Design Concepts ◽  
Flexible Designs ◽  
Gauss Points

AbstractThis paper presents a new FE-based stress-related topology optimization approach for finding bending governed flexible designs. Thereby, the knowledge about an output displacement or force as well as the detailed mounting position is not necessary for the application. The newly developed objective function makes use of the varying stress distribution in the cross section of flexible structures. Hence, each element of the design space must be evaluated with respect to its stress state. Therefore, the method prefers elements experiencing a bending or shear load over elements which are mainly subjected to membrane stresses. In order to determine the stress state of the elements, we use the principal stresses at the Gauss points. For demonstrating the feasibility of the new topology optimization approach, three academic examples are presented and discussed. As a result, the developed sensitivity-based algorithm is able to find usable flexible design concepts with a nearly discrete 0 − 1 density distribution for these examples.

Discovering Sequenced Origami Folding Through Nonlinear Mechanics and Topology Optimization

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Andrew S. Gillman ◽  
Kazuko Fuchi ◽  
Philip R. Buskohl
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Optimization Algorithms ◽  
Element Model ◽  
Evolutionary Optimization ◽  
Nonlinear Mechanics ◽  
Design Problems ◽  
Mechanics Model ◽  
Highly Nonlinear ◽  
Evolutionary Optimization Algorithms

Origami folding provides a novel method to transform two-dimensional (2D) sheets into complex functional structures. However, the enormity of the foldable design space necessitates development of algorithms to efficiently discover new origami fold patterns with specific performance objectives. To address this challenge, this work combines a recently developed efficient modified truss finite element model with a ground structure-based topology optimization framework. A nonlinear mechanics model is required to model the sequenced motion and large folding common in the actuation of origami structures. These highly nonlinear motions limit the ability to define convex objective functions, and parallelizable evolutionary optimization algorithms for traversing nonconvex origami design problems are developed and considered. The ability of this framework to discover fold topologies that maximize targeted actuation is verified for the well-known “Chomper” and “Square Twist” patterns. A simple twist-based design is also discovered using the verified framework. Through these case studies, the role of critical points and bifurcations emanating from sequenced deformation mechanisms (including interplay of folding, facet bending, and stretching) on design optimization is analyzed. In addition, the performance of both gradient and evolutionary optimization algorithms are explored, and genetic algorithms (GAs) consistently yield solutions with better performance given the apparent nonconvexity of the response-design space.

Performance Oriented Design of Semiregular Anisotropic Porous Structures

2018 ◽  
Author(s):  
Chao Xu ◽  
Lili Pan ◽  
Ming Li ◽  
Shuming Gao
Keyword(s):  
3D Printing ◽  
Porous Materials ◽  
Design Problem ◽  
Degrees Of Freedom ◽  
Design Space ◽  
Manufacturing Technology ◽  
Porous Structures ◽  
Precise Control ◽  
And Performance

Porous materials / structures have wide applications in industry, since the sizes, shapes and positions of their pores can be adjusted on various demands. However, the precise control and performance oriented design of porous structures are still urgent and challenging, especially when the manufacturing technology is well developed due to 3D printing. In this study, the control and design of anisotropic porous structures are studied with more degrees of freedom than isotropic structures, and can achieve more complex mechanical goals. The proposed approach introduces Super Formula to represent the structural cells, maps the design problem to an optimal problem using PGD, and solves the optimal problem using MMA to obtain the structure with desired performance. The proposed approach is also tested on the performance of the expansion of design space, the capture of the physical orientation and so on.

Large-scale three-dimensional anisotropic topology optimization of variable-axial lightweight composite structures

2021 ◽  
pp. 1-15
Author(s):  
Yuqing Zhou ◽  
Tsuyoshi Nomura ◽  
Enpei Zhao ◽  
Kazuhiro Saitou
Keyword(s):  
Topology Optimization ◽  
Composite Structures ◽  
Large Scale ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Optimization Method ◽  
Optimized Design ◽  
Adaptive Meshing ◽  
Design Synthesis ◽  
Fiber Placement

Abstract Variable-axial fiber-reinforced composites allow for local customization of fiber orientation and thicknesses. Despite their significant potential for performance improvement over the conventional multiaxial composites and metals, they pose challenges in design optimization due to the vastly increased design freedom in material orientations. This paper presents an anisotropic topology optimization method for designing large-scale, 3D variable-axial lightweight composite structures subject to multiple load cases. The computational challenges associated with large-scale 3D anisotropic topology optimization with extremely low volume fraction are addressed by a tensor-based representation of 3D orientation that would avoid the 2π periodicity of angular representations such as Euler angles, and an adaptive meshing scheme, which, in conjunction with PDE regularization of the density variables, refines the mesh where structural members appear and coarsens where there is void. The proposed method is applied to designing a heavy-duty drone frame subject to complex multi-loading conditions. Finally, the manufacturability gaps between the optimized design and the fabrication-ready design for Tailored Fiber Placement (TFP) is discussed, which motivates future work toward a fully-automated design synthesis.

scholarly journals Impact Response of Hammerhead Pier Fibrous Concrete Beams Designed with Topology Optimization

2020 ◽  
Author(s):  
Meivazhisalai Parasuraman Salaimanimagudam ◽  
Covaty Ravi Suribabu ◽  
Gunasekaran Murali ◽  
Sallal R. Abid
Keyword(s):  
Topology Optimization ◽  
Concrete Beams ◽  
Impact Load ◽  
Impact Resistance ◽  
Adaptive Mesh ◽  
Impact Response ◽  
Adaptive Meshing ◽  
Repeated Impact ◽  
Ductility Ratio ◽  
The Impact

Reducing the weight of concrete beams is a primary (beyond strength and durability) concern of engineers. Therefore, this research was directed to investigate the impact response of hammerhead pier concrete beams designed with density-based method topology optimization. The finite element topology optimization was conducted using Autodesk fusion 360 considering three different mesh sizes of 7 mm, 10 mm, and adaptive meshing. Three optimized hammerhead beam configurations; HB1, HB2, and HB3, respectively, with volume reductions greater than 50 %. In the experimental part of this research, nine beams were cast with identical size and configuration to the optimized beams. Three beams, identical to the optimized beams, were tested under static bending for verification purposes. In comparison, six more beams, as in the preceding three beams but without and with hooked end steel fibers, were tested under repeated impact load. The test results revealed that the highest flexural capacity and impact resistance at crack initiation and failure were recorded for the adaptive mesh beams (HB3 and HB3SF). The failure impact energy and ductility ratio of the beam HB3SF was higher than the beams HB1SF and HB2SF by more than 270 %. The results showed that the inclusion of steel fiber duplicated the optimized beam’s impact strength and ductility several times. The failure impact resistance of fibrous beams was higher than their corresponding plain beams by approximately 2300 to4460 %, while their impact ductility ratios were higher by 6.0 to 18.1 times.

Investigation of Parameter Spaces for Topology Optimization With Three-Dimensional Orientation Fields for Multi-Axis Additive Manufacturing

2020 ◽  
Vol 143 (5) ◽  
Author(s):  
Joseph R. Kubalak ◽  
Alfred L. Wicks ◽  
Christopher B. Williams
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Design Space ◽  
Mechanical Performance ◽  
Unit Length ◽  
Three Dimensions ◽  
Layer By Layer ◽  
Material Distribution ◽  
Orientation Fields ◽  
Material Orientation

Abstract The layer-by-layer deposition process used in material extrusion (ME) additive manufacturing results in inter- and intra-layer bonds that reduce the mechanical performance of printed parts. Multi-axis (MA) ME techniques have shown potential for mitigating this issue by enabling tailored deposition directions based on loading conditions in three dimensions (3D). Planning deposition paths leveraging this capability remains a challenge, as an intelligent method for assigning these directions does not exist. Existing literature has introduced topology optimization (TO) methods that assign material orientations to discrete regions of a part by simultaneously optimizing material distribution and orientation. These methods are insufficient for MA–ME, as the process offers additional freedom in varying material orientation that is not accounted for in the orientation parameterizations used in those methods. Additionally, optimizing orientation design spaces is challenging due to their non-convexity, and this issue is amplified with increased flexibility; the chosen orientation parameterization heavily impacts the algorithm’s performance. Therefore, the authors (i) present a TO method to simultaneously optimize material distribution and orientation with considerations for 3D material orientation variation and (ii) establish a suitable parameterization of the orientation design space. Three parameterizations are explored in this work: Euler angles, explicit quaternions, and natural quaternions. The parameterizations are compared using two benchmark minimum compliance problems, a 2.5D Messerschmitt–Bölkow–Blohm beam and a 3D Wheel, and a multi-loaded structure undergoing (i) pure tension and (ii) three-point bending. For the Wheel, the presented algorithm demonstrated a 38% improvement in compliance over an algorithm that only allowed planar orientation variation. Additionally, natural quaternions maintain the well-shaped design space of explicit quaternions without the need for unit length constraints, which lowers computational costs. Finally, the authors present a path toward integrating optimized geometries and material orientation fields resulting from the presented algorithm with MA–ME processes.

Large-Scale Three-Dimensional Anisotropic Topology Optimization of Variable-Axial Composite Structures

2020 ◽  
Author(s):  
Yuqing Zhou ◽  
Tsuyoshi Nomura ◽  
Enpei Zhao ◽  
Wei Zhang ◽  
Kazuhiro Saitou
Keyword(s):  
Topology Optimization ◽  
Composite Structures ◽  
Large Scale ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Optimized Design ◽  
Adaptive Meshing ◽  
Design Synthesis ◽  
Fiber Placement ◽  
Future Work

Abstract Variable-axial fiber-reinforced composites allow for local customization of fiber orientation and thicknesses. Despite their significant potential for performance improvement over the conventional multiaxial composites and metals, they pose challenges in design optimization due to the vastly increased design freedom in material orientations. This paper presents an anisotropic topology optimization (TO) method for designing large-scale, 3D variable-axial composite structures. The computational challenge for large-scale 3D TO with extremely low volume fraction is addressed by a tensor-based representation of 3D orientation that would avoid the 2π periodicity of angular representation such as Eular angles, and an adaptive meshing scheme, which, in conjunction with PDE regularization of the density variables, refines the mesh where structural members appear and coarsens where there is void. The proposed method is applied to designing a heavy-duty drone frame subject to complex multi-loading conditions. Finally, the manufacturability gaps between the optimized design and the fabrication-ready design for Tailored Fiber Placement (TFP) is discussed, which motivates future work toward fully-automated design synthesis.

Topology and Free Size Optimization With Manufacturing Constraints for Light Weight Die Cast Automotive Backrest Frame

2009 ◽  
Author(s):  
Sreeram Polavarapu ◽  
Lonny L. Thompson ◽  
Mica Grujicic
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Design Space ◽  
Size Optimization ◽  
Manufacturing Constraints ◽  
Material Distribution ◽  
Front Seat ◽  
Die Cast ◽  
Stiffening Ribs ◽  
Multiple Load

Finite element analysis, together with topology and free-size optimization is used to design a lightweight die cast automotive front seat backrest frame when subjected to loads prescribed by ECE R17 European government regulations and additional loads which are predicted in an event of crash. In particular, an effort is made here to study the characteristics of a die cast automotive front seat backrest frame and develop a method for predicting the optimized material and support rib distribution which provides a lightweight seat which satisfies both strength and deflection requirements in a design space which includes the action of multiple load cases. An existing commercially available die cast backrest frame serves as the reference design space. Both 3D surface and solid models are created for representation as shell and solid finite element models for analysis. The objective function for topology optimization of the 3D solid model is to minimize mass of the component subject to stress and deflection constraints and is used as a guide in determining optimal geometric distribution of stiffening ribs. When the shell model of the reference seat is subjected to free-size optimization with this same constraint and objective given, an optimized material distribution measured by shell element thicknesses is obtained. For the topology optimization, manufacturing constraints of preferred draw direction and symmetry are applied in order to obtain an optimized material distribution which can be manufactured in the die-cast process. The procedure followed in this work generated an optimal material distribution and stiffening ribs in a lightweight die cast automotive seat backrest frame when subjected to multiple load cases. An overall reduction in weight of 13% is achieved over a reference commercially available die cast backrest frame component.

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