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1. Topology optimization of shape memory polymer structures with programmable morphology

   https://doi.org/10.1007/s00158-020-02784-0  

   Bhattacharyya, Anurag ; James, Kai A. ( February 2021 , Structural and Multidisciplinary Optimization)

   null (Ed.)

   We present a novel optimization framework for optimal design of structures exhibiting memory characteristics by incorporating shape memory polymers (SMPs). SMPs are a class of memory materials capable of undergoing and recovering applied deformations. A finite-element analysis incorporating the additive decomposition of small strain is implemented to analyze and predict temperature-dependent memory characteristics of SMPs. The finite element method consists of a viscoelastic material modelling combined with a temperature-dependent strain storage mechanism, giving SMPs their characteristic property. The thermo-mechanical characteristics of SMPs are exploited to actuate structural deflection to enable morphing toward a target shape. A time-dependent adjoint sensitivity formulation implemented through a recursive algorithm is used to calculate the gradients required for the topology optimization algorithm. Multimaterial topology optimization combined with the thermo-mechanical programming cycle is used to optimally distribute the active and passive SMP materials within the design domain. This allows us to tailor the response of the structures to design them with specific target displacements, by exploiting the difference in the glass-transition temperatures of the two SMP materials. Forward analysis and sensitivity calculations are combined in a PETSc-based optimization framework to enable efficient multi-functional, multimaterial structural design with controlled deformations. 

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2. Thermomechanical topology optimization of shape‐memory alloy structures using a transient bilevel adjoint method

   https://doi.org/10.1002/nme.6319  

   Kang, Ziliang ; James, Kai A. ( February 2020 , International Journal for Numerical Methods in Engineering)

   We present a novel method for computational design of adaptive shape‐memory alloy (SMA) structures via topology optimization. By optimally distributing a SMA within the prescribed design domain, the proposed algorithm seeks to tailor the two‐way shape‐memory effect (TWSME) and pseudoelasticity response of the SMA materials. Using a phenomenological material model, the thermomechanical response of the SMA structure is solved through inelastic finite element analysis, while assuming a transient but spatially uniform temperature distribution. The material distribution is parameterized via a SIMP formulation, with gradient‐based optimization used to perform the optimization search. We derive a transient, bilevel adjoint formulation for analytically computing the design sensitivities. We demonstrate the proposed design framework using a series of two‐dimensional thermomechanical benchmark problems. These examples include design for optimal displacement due to the TWSME, and design for maximum mechanical advantage while accounting for pseudoelasticity.

    

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3. A Fluid-Structure Coupled Computational Model for the Certification of Shock-Resistant Elastomer Coatings

   https://doi.org/10.1115/OMAE2020-18501  

   Ma, Wentao ; Zhao, Xuning ; Wang, Kevin ( August 2020 , ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering)

   null (Ed.)

   Shock waves from underwater and air explosions are significant threats to surface and underwater vehicles and structures. Recent studies on the mechanical and thermal properties of various phase-separated elastomers indicate the possibility of applying these materials as a coating to mitigate shock-induced structural failures. To demonstrate this approach and investigate its efficacy, this paper presents a fluid-structure coupled computational model capable of predicting the dynamic response of air-backed bilayer (i.e. elastomer coating – metal substrate) structures submerged in water to hydrostatic and underwater explosion loads. The model couples a three-dimensional multiphase finite volume computational fluid dynamics model with a nonlinear finite element computational solid dynamics model using the FIVER (FInite Volume method with Exact multi-material Riemann solvers) method. The kinematic boundary condition at the fluid-structure interface is enforced using an embedded boundary method that is capable of handling large structural deformation and topological changes. The dynamic interface condition is enforced by formulating and solving local, one-dimensional fluid-solid Riemann problems, which is well-suited for transferring shock and impulsive loads. The capability of this computational model is demonstrated through a numerical investigation of hydrostatic and shock-induced collapse of aluminum tubes with polyurea coating on its inner surface. The thickness of the structure is resolved explicitly by the finite element mesh. The nonlinear material behavior of polyurea is accounted for using a hyper-viscoelastic constitutive model featuring a modified Mooney-Rivlin equation and a stress relaxation function in the form of prony series. Three numerical experiments are conducted to simulate and compare the collapse of the structure in different loading conditions, including a constant pressure, a fluid environment initially in hydrostatic equilibrium, and a two-phase fluid flow created by a near-field underwater explosion.

    

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4. Virtual element method (VEM)-based topology optimization: an integrated framework

   https://doi.org/10.1007/s00158-019-02268-w  

   Chi, Heng ; Pereira, Anderson ; Menezes, Ivan F. ; Paulino, Glaucio H. ( October 2020 , Structural and Multidisciplinary Optimization)

   We present a virtual element method (VEM)-based topology optimization framework using polyhedral elements, which allows for convenient handling of non-Cartesian design domains in three dimensions. We take full advantage of the VEM properties by creating a unified approach in which the VEM is employed in both the structural and the optimization phases. In the structural problem, the VEM is adopted to solve the three-dimensional elasticity equation. Compared to the finite element method, the VEM does not require numerical integration (when linear elements are used) and is less sensitive to degenerated elements (e.g., ones with skinny faces or small edges). In the optimization problem, we introduce a continuous approximation of material densities using the VEM basis functions. When compared to the standard element-wise constant approximation, the continuous approximation enriches the geometrical representation of structural topologies. Through two numerical examples with exact solutions, we verify the convergence and accuracy of both the VEM approximations of the displacement and material density fields. We also present several design examples involving non-Cartesian domains, demonstrating the main features of the proposed VEM-based topology optimization framework. The source code for a MATLAB implementation of the proposed work, named PolyTop3D, is available in the (electronic) Supplementary Material accompanying this publication. 

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5. A spatially varying robin interface condition for fluid‐structure coupled simulations

   https://doi.org/10.1002/nme.6386  

   Cao, Shunxiang ; Wang, Guangyao ; Wang, Kevin G. ( August 2020 , International Journal for Numerical Methods in Engineering)

   We present a spatially varying Robin interface condition for solving fluid‐structure interaction problems involving incompressible fluid flows and nonuniform flexible structures. Recent studies have shown that for uniform structures with constant material and geometric properties, a constant one‐parameter Robin interface condition can improve the stability and accuracy of partitioned numerical solution procedures. In this work, we generalize the parameter to a spatially varying function that depends on the structure's local material and geometric properties, without varying the exact solution of the coupled fluid‐structure system. We present an algorithm to implement the Robin interface condition in an embedded boundary method for coupling a projection‐based incompressible viscous flow solver with a nonlinear finite element structural solver. We demonstrate the numerical effects of the spatially varying Robin interface condition using two example problems: a simplified model problem featuring a nonuniform Euler‐Bernoulli beam interacting with an inviscid flow and a generalized Turek‐Hron problem featuring a nonuniform, highly flexible beam interacting with a viscous laminar flow. Both cases show that a spatially varying Robin interface condition can clearly improve numerical accuracy (by up to two orders of magnitude in one instance) for the same computational cost. Using the second example problem, we also demonstrate and compare two models for determining the local value of the combination function in the Robin interface condition.

    

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