Topology Optimization of Cellular Materials With Maximized Energy Absorption

2015 ◽  
Author(s):  
Josephine V. Carstensen ◽  
Reza Lotfi ◽  
James K. Guest ◽  
Wen Chen ◽  
Jan Schroers
Keyword(s):  
Topology Optimization ◽  
Mathematical Programming ◽  
Energy Absorption ◽  
High Performance ◽  
Optimization Problem ◽  
Cellular Materials ◽  
Component Level ◽  
Linear Elastic ◽  
Optimization Formulation ◽  
Level Scale

While topology optimization is typically employed for design at the component-level scale, it is increasingly being used to design the topology of high performance cellular materials. The design problem is posed as an optimization problem with governing unit cell and upscaling mechanics embedded in the formulation, and solved with formal mathematical programming. While design for linear elastic properties is generally well-established, this paper will discuss including nonlinear mechanics in the topology optimization formulation, also in the domain of cellular materials. In particular, the problem of maximizing total energy absorption of a cellular Bulk Metallic Glass material is considered and numerical and experimental analyses of the new design show that it has enhanced performance compared to conventional cellular topologies.

Topology Optimization for Cellular Material Design

2014 ◽  
Vol 1662 ◽  
Author(s):  
Reza Lotfi ◽  
Seunghyun Ha ◽  
Josephine V. Carstensen ◽  
James K. Guest
Keyword(s):  
Topology Optimization ◽  
Mathematical Programming ◽  
High Performance ◽  
Optimization Problem ◽  
Material Design ◽  
Cellular Materials ◽  
Computational Approach ◽  
Manufacturing Processes ◽  
Component Level ◽  
Level Scale

ABSTRACTTopology optimization is a systematic, computational approach to the design of structure, defined as the layout of materials (and pores) across a domain. Typically employed at the component-level scale, topology optimization is increasingly being used to design the architecture of high performance materials. The resulting design problem is posed as an optimization problem with governing unit cell and upscaling mechanics embedded in the formulation, and solved with formal mathematical programming. This paper will describe recent advances in topology optimization, including incorporation of manufacturing processes and objectives governed by nonlinear mechanics and multiple physics, and demonstrate their application to the design of cellular materials. Optimized material architectures are shown to (computationally) approach theoretical bounds when available, and can be used to generate estimations of bounds when such bounds are unknown.

Topology Optimization of the Fiber-Reinforcement of No-Tension Masonry Walls

2017 ◽  
Vol 747 ◽  
pp. 36-43 ◽  
Author(s):  
Matteo Bruggi ◽  
Alberto Taliercio
Keyword(s):  
Topology Optimization ◽  
Optimization Problem ◽  
Fiber Reinforcement ◽  
Masonry Walls ◽  
Constrained Optimization Problem ◽  
Principal Stresses ◽  
Linear Elastic ◽  
Optimal Reinforcement ◽  
Optimization Formulation ◽  
Perfect Bonding

An innovative approach is proposed to define the optimal fiber-reinforcement of in-plane loaded masonry walls, modeled as linear elastic no-tension (NT) bodies. A topology optimization formulation is presented, which aims at distributing a prescribed amount of reinforcement over the wall, so as to minimize the overall elastic energy of the strengthened element. Perfect bonding is assumed at the wall-reinforcement interface. To account for the negligible tensile strength of brickwork, the material is replaced by an equivalent orthotropic material with negligible stiffness along the direction (s) undergoing tensile principal stress (es). Compressive principal stresses in the reinforcement are not allowed. A single constrained optimization problem allows both the equilibrium of the NT body to be enforced, and the optimal reinforcing layout to be spotted out, without any demanding incremental approach. Some preliminary numerical examples are shown to assess the capabilities of the proposed procedure and to identify the optimal reinforcement patterns for common types of masonry walls with openings.

scholarly journals An Efficient Topology Description Function Method Based on Modified Sigmoid Function

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xingfa Yang ◽  
Jie Liu ◽  
Yin Yang ◽  
Qixiang Qing ◽  
Guilin Wen
Keyword(s):  
Topology Optimization ◽  
Function Method ◽  
Optimization Problem ◽  
Optimization Methods ◽  
Heaviside Function ◽  
Sigmoid Function ◽  
Topology Optimization Problem ◽  
Linear Elastic ◽  
Topology Description Function ◽  
Structural Compliance

Optimal geometries extracted from traditional element-based topology optimization outcomes usually have zigzag boundaries, leading to being difficult to fabricate. In this study, a fairly accurate and efficient topology description function method (TDFM) for topology optimization of linear elastic structures is developed. By employing the modified sigmoid function, a simple yet efficient strategy is presented to tackle the computational difficulties because of the nonsmoothness of Heaviside function in topology optimization problem. The optimization problem is to minimize the structural compliance, with highest stiffness, while satisfying the volume constraint. The design problem is solved by a Sequential Linear Programming method. Convergent, crisp, and smooth final layouts are obtained, which can be fabricated without postprocessing, demonstrated by a series of numerical examples. Further, the proposed method has a rather higher accuracy and efficiency compared with traditional TDFM, when the classical topology optimization methods, such as bidirectional evolutionary structural optimization (BESO) and solid isotropic material with penalization (SIMP) method, are taken as benchmark.

scholarly journals A Review on Tailoring Stiffness in Compliant Systems, via Removing Material: Cellular Materials and Topology Optimization

2021 ◽  
Vol 11 (8) ◽  
pp. 3538
Author(s):  
Mauricio Arredondo-Soto ◽  
Enrique Cuan-Urquizo ◽  
Alfonso Gómez-Espinosa
Keyword(s):  
Mechanical Properties ◽  
Topology Optimization ◽  
Evolutionary Process ◽  
Cellular Materials ◽  
Related Literature ◽  
And Topology ◽  
Fundamental Process ◽  
Compliant Systems ◽  
Basic Concepts

Cellular Materials and Topology Optimization use a structured distribution of material to achieve specific mechanical properties. The controlled distribution of material often leads to several advantages including the customization of the resulting mechanical properties; this can be achieved following these two approaches. In this work, a review of these two as approaches used with compliance purposes applied at flexure level is presented. The related literature is assessed with the aim of clarifying how they can be used in tailoring stiffness of flexure elements. Basic concepts needed to understand the fundamental process of each approach are presented. Further, tailoring stiffness is described as an evolutionary process used in compliance applications. Additionally, works that used these approaches to tailor stiffness of flexure elements are described and categorized. Finally, concluding remarks and recommendations to further extend the study of these two approaches in tailoring the stiffness of flexure elements are discussed.

Efficient Sensitivity Analysis for Multibody Dynamics Systems Using an Iterative Steps Method With Application in Topology Optimization

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi ◽  
Sudhakar Arepally ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Multibody Dynamics ◽  
Optimization Problem ◽  
Finite Difference Methods ◽  
Analysis Method ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Rotational Motions

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

Lessons from Nature for the Construction of Ceramic Cellular Materials for Superior Energy Absorption

2011 ◽  
Vol 13 (11) ◽  
pp. 1042-1049 ◽  
Author(s):  
Volker Presser ◽  
Stefanie Schultheiß ◽  
Christian Kohler ◽  
Christoph Berthold ◽  
Klaus G. Nickel ◽  
...  
Keyword(s):  
Energy Absorption ◽  
Cellular Materials

Topology Optimization for the Single Phase Flow Using Two Point Flux Approximation Model

2013 ◽  
Author(s):  
Guang Dong ◽  
Yulan Song
Keyword(s):  
Porous Media ◽  
Topology Optimization ◽  
Optimization Problem ◽  
Single Phase ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Approximation Model ◽  
Single Phase Flow ◽  
Topology Optimization Problem ◽  
Flux Approximation

The topology optimization method is extended to solve a single phase flow in porous media optimization problem based on the Two Point Flux Approximation model. In particular, this paper discusses both strong form and matrix form equations for the flow in porous media. The design variables and design objective are well defined for this topology optimization problem, which is based on the Solid Isotropic Material with Penalization approach. The optimization problem is solved by the Generalized Sequential Approximate Optimization algorithm iteratively. To show the effectiveness of the topology optimization in solving the single phase flow in porous media, the examples of two-dimensional grid cell TPFA model with impermeable regions as constrains are presented in the numerical example section.

Multifunctional Topology Design of Cellular Material Structures

2006 ◽  
Author(s):  
Carolyn Conner Seepersad ◽  
Janet K. Allen ◽  
David L. McDowell ◽  
Farrokh Mistree
Keyword(s):  
Heat Transfer ◽  
Topology Optimization ◽  
Cell Walls ◽  
Cellular Structure ◽  
Optimization Methods ◽  
Cellular Materials ◽  
Design Methods ◽  
Topology Design ◽  
Cellular Topology ◽  
Multifunctional Properties

Prismatic cellular or honeycomb materials exhibit favorable properties for multifunctional applications such as ultra-light load bearing combined with active cooling. Since these properties are strongly dependent on the underlying cellular structure, design methods are needed for tailoring cellular topologies with customized multifunctional properties that may be unattainable with standard cell designs. Topology optimization methods are available for synthesizing the form of a cellular structure—including the size, shape, and connectivity of cell walls and the number, shape, and arrangement of cell openings—rather than specifying these features a priori. To date, the application of these methods for cellular materials design has been limited primarily to elastic and thermo-elastic properties, however, and limitations of standard topology optimization methods prevent direct application to many other phenomena such as conjugate heat transfer with internal convection. In this paper, we introduce a practical, two-stage, flexibility-based, multifunctional topology design approach for applications that require customized multifunctional properties. As part of the approach, robust topology design methods are used to design flexible cellular topology with customized structural properties. Dimensional and topological flexibility is embodied in the form of robust ranges of cell wall dimensions and robust permutations of a nominal cellular topology. The flexibility is used to improve the heat transfer characteristics of the design via addition/removal of cell walls and adjustment of cellular dimensions, respectively, without degrading structural performance. We apply the method to design stiff, actively cooled prismatic cellular materials for the combustor liners of next-generation gas turbine engines.

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