Abstract
This paper presents a new discrete parametrization method for simultaneous topology and material optimization of composite laminate structures, referred to as Hyperbolic Function Parametrization (HFP). The novelty of HFP is the way the candidate materials are parametrized in the optimization problem. In HFP, a filtering technique based on hyperbolic functions is used, such that only one design variable is used for any given number of material candidates. Compared to state-of-the-art methods such Discrete Material and Topology Optimization (DMTO) and Shape Function with Penalization (SFP), HFP has much fewer optimization variables and constraints but introduces additional non-linearity in the optimization problems. A comparative analysis of HFP, DMTO and SFP are performed based on the problem of maximizing the stiffness of composite plates under a total volume constraint and multiple manufacturing constraints using various loads, boundary conditions and input parameters. The comparison shows that all three methods are highly sensitive to the choice of input parameters for the optimization problem, although the performance of HFP is overall more consistent. HFP method performs similarly to DMTO and SFP in terms of the designs obtained and computational cost. However, HFP obtains similar or better objective function values compared to the DMTO and SFP methods.
Highlights
Composite materials are known to have superior strength-to-weight and stiffness-to-weight properties compared to e.g. metallic materials
The optimization problems involve a large number of parameters which may affect the performance of the parametrization methods
Compared to existing state-of-art parametrization methods such as Discrete Material and Topology Optimization (DMTO) and Shape Function with Penalization (SFP), Hyperbolic Function Parametrization (HFP) reduces the size of the optimization problem both in terms of number of design variable and constraints, this comes at the cost of introducing addi tional non-linearity in the optimization problem
Summary
Composite materials are known to have superior strength-to-weight and stiffness-to-weight properties compared to e.g. metallic materials These properties, along with the inherent ability to enable tailoring of mechanical behavior of structures, have been the primary motivation for choosing composites in manufacturing of products and structural com ponents. The past two decades have seen a rapid development of new and innovative composite manufacturing technologies and an increased availability of diverse and cost-effective composite materials This has resulted in a substantial growth in application of composites within industrial sectors such as aerospace, energy generation, infrastructure, heavy industry and automotive. Structural optimization is often utilized in an attempt to handle all parameters, requirements and limitations in the design of composite structures This requires an efficient parametriza tion scheme of the relevant variables to generate optimal and manu facturable designs. This has resulted in a significant body of work concerning composite parametrization techniques performed within the field of structural optimization over the years
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