Evolutionary topology optimization of continuum structures using X-FEM and isovalues of structural performance

In the last three decades, advances in modern manufacturing processes, such as additive manufacturing (AM) on one hand and computational power on the other hand, has resulted in a surge of interest in topology optimization as a means of designing high performance components with high degrees of geometrical complexity. Topology optimization seeks to find the best design for a structure by optimally distributing material in a design space. Therefore not only the shape and size of the structure, but also the connectivity of the structure changes during the topology optimization process. As a result, the solution of a topology optimization problem might be represented with a high degree of geometrical complexity as it is not dependent on the initial geometry. The finite element method (FEM) is a powerful numerical analysis technique that was developed to solve complex solid mechanics problems. Many topology optimization approaches use FEM to calculate the response of the structure during the optimization process and some of them, called “element based-methods”, are integrated with FEM to use the properties of finite elements as design variables in the optimization. The solutions of such approaches are usually represented by a uniform finite element mesh that bears no relation to the final geometry and hence they don’t provide an accurate representation of the design boundary. The solution from topology optimization must therefore go through further post processing stages to obtain a manufacturable design. The post processing stages which can include smoothing and shape optimization are costly and time-consuming and may result in the structure becoming less optimal. With traditional manufacturing processes this is acceptable as the manufacturing constraints prevent the optimized design from being manufactured so some re-analysis is necessary. With additive manufacturing, however, this restriction is removed, which means a topology optimization resulting in a manufacturable design is highly desirable. Evolutionary structural optimization (ESO) is an element based topology optimization approach which operates by systematically removing inefficient material from the structure until the optimization objective achieves convergence. Due to the intuitive nature of ESO, this method is simple to be programed and can be easily integrated with FEM or other numerical analysis techniques; thus it is suitable for complex geometries represented with FEM. During the last two decades ESO and its extensions, such as bi-directional ESO (BESO), have been successfully used for many topology optimization problems such as stiffness design, design of compliant mechanisms, heat conduction problems and frequency problems. However, being an element based method, the drawback of poor boundary representation remains. The extended finite element method (X-FEM) is an extension of the classical FEM that was developed to represent discontinuities, such as cracks and material-void interfaces, inside finite elements. X-FEM can be employed in topology optimization problems to handle the material-void discontinuity introduced by the evolving boundary during the optimization process which potentially enables a sub-element boundary representation. This requires an implicit boundary representation, such as level-set method with the benefits of better computational accuracy through the optimization, more optimized solution and smoother boundaries for direct to manufacture. In this work a new method of evolutionary structural optimization is proposed in which X-FEM is employed for the more smooth and accurate representation of the design boundary. Linear finite elements are used to discretize the design space. These include 4-node quadrilateral elements in 2D modelling and 8-node hexahedral elements in 3D modelling. To implement the X-FEM, an implicit boundary representation using isoline and isosurface approaches is used. The proposed method which is called “Iso-XFEM” is implemented for various topology optimization problems, including the stiffness design of 2D and 3D structures, stiffness design with additional displacement constraint and topology optimization of geometrically nonlinear problems. The solutions of the Iso-XFEM method are compared with those obtained using BESO, as a representative FE based method. The results confirm a significant improvement in boundary representation of the solutions when compared against BESO, and also demonstrate the feasibility of the application of the proposed method to complex real-life structures and to different objectives. All the programs used to generate topology optimised solutions using the proposed method and its modifications are developed by the author. These include topology optimization codes, linear and non-linear FEA, and 2D and 3D X-FEM integration schemes

Evolutionary topology optimization of continuum structures using X-FEM and isovalues of structural performance

In the last three decades, advances in modern manufacturing processes, such as additive manufacturing (AM) on one hand and computational power on the other hand, has resulted in a surge of interest in topology optimization as a means of designing high performance components with high degrees of geometrical complexity. Topology optimization seeks to find the best design for a structure by optimally distributing material in a design space. Therefore not only the shape and size of the structure, but also the connectivity of the structure changes during the topology optimization process. As a result, the solution of a topology optimization problem might be represented with a high degree of geometrical complexity as it is not dependent on the initial geometry. The finite element method (FEM) is a powerful numerical analysis technique that was developed to solve complex solid mechanics problems. Many topology optimization approaches use FEM to calculate the response of the structure during the optimization process and some of them, called “element based-methods”, are integrated with FEM to use the properties of finite elements as design variables in the optimization. The solutions of such approaches are usually represented by a uniform finite element mesh that bears no relation to the final geometry and hence they don’t provide an accurate representation of the design boundary. The solution from topology optimization must therefore go through further post processing stages to obtain a manufacturable design. The post processing stages which can include smoothing and shape optimization are costly and time-consuming and may result in the structure becoming less optimal. With traditional manufacturing processes this is acceptable as the manufacturing constraints prevent the optimized design from being manufactured so some re-analysis is necessary. With additive manufacturing, however, this restriction is removed, which means a topology optimization resulting in a manufacturable design is highly desirable. Evolutionary structural optimization (ESO) is an element based topology optimization approach which operates by systematically removing inefficient material from the structure until the optimization objective achieves convergence. Due to the intuitive nature of ESO, this method is simple to be programed and can be easily integrated with FEM or other numerical analysis techniques; thus it is suitable for complex geometries represented with FEM. During the last two decades ESO and its extensions, such as bi-directional ESO (BESO), have been successfully used for many topology optimization problems such as stiffness design, design of compliant mechanisms, heat conduction problems and frequency problems. However, being an element based method, the drawback of poor boundary representation remains. The extended finite element method (X-FEM) is an extension of the classical FEM that was developed to represent discontinuities, such as cracks and material-void interfaces, inside finite elements. X-FEM can be employed in topology optimization problems to handle the material-void discontinuity introduced by the evolving boundary during the optimization process which potentially enables a sub-element boundary representation. This requires an implicit boundary representation, such as level-set method with the benefits of better computational accuracy through the optimization, more optimized solution and smoother boundaries for direct to manufacture. In this work a new method of evolutionary structural optimization is proposed in which X-FEM is employed for the more smooth and accurate representation of the design boundary. Linear finite elements are used to discretize the design space. These include 4-node quadrilateral elements in 2D modelling and 8-node hexahedral elements in 3D modelling. To implement the X-FEM, an implicit boundary representation using isoline and isosurface approaches is used. The proposed method which is called “Iso-XFEM” is implemented for various topology optimization problems, including the stiffness design of 2D and 3D structures, stiffness design with additional displacement constraint and topology optimization of geometrically nonlinear problems. The solutions of the Iso-XFEM method are compared with those obtained using BESO, as a representative FE based method. The results confirm a significant improvement in boundary representation of the solutions when compared against BESO, and also demonstrate the feasibility of the application of the proposed method to complex real-life structures and to different objectives. All the programs used to generate topology optimised solutions using the proposed method and its modifications are developed by the author. These include topology optimization codes, linear and non-linear FEA, and 2D and 3D X-FEM integration schemes

Design optimization for an additively manufactured automotive component

The aim of this paper is to investigate the design optimization and additive manufacture of automotive components. A Titanium brake pedal processed through Selective Laser Melting (SLM) is considered as a test case. Different design optimisation techniques have been employed including topology optimization and lattice structure design. Rather than using a conventional topology optimization method, a recently developed topology optimization method called Iso-XFEM is used in this work. This method is capable of generating high resolution topology optimised solutions using isolines/isosurfaces of a structural performance criterion and eXtended Finite Element Method (XFEM). Lattice structure design is the other technique used in this work for the design of the brake pedal. The idea is to increase the stability of the brake pedal to random loads applied to the foot pad area of the pedal. The use of lattice structures can also significantly reduce the high residual stress induced during the SLM process. The results suggest that the integration of the design optimization techniques with a metal additive manufacturing process enables development of a promising tool for producing lightweight energy efficient automotive components

Investigation of passive oscillations of flexible splitter plates attached to a circular cylinder

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This paper presents a numerical study to address wake control of a circular cylinder subjected to two-dimensional laminar flow regime using single and multiple flexible splitter plates attached to the cylinder. Three different cases are presented in the study, covering cylinders with one, two and three horizontally attached splitter plates while the locations of the plates around the cylinders are varied. The length of the splitter plates was equal to the cylinder diameter and Reynolds number was 100. Due to the flexibility of the plates, the problem was modeled as a Fluid-Structure Interaction (FSI) problem and the commercial finite element software, Comsol Multiphysics, was utilized to solve this problem using Arbitrary Lagrangian–Eulerian (ALE) method. Vortex shedding frequency and fluid forces acting on the cylinder are investigated, along with a comprehensive parametric study to identify the optimum arrangement of the plates for maximum drag reduction and maximum vortex shedding frequency reduction. The numerical results associated to the flexible splitter plates are also compared with the corresponding rigid splitter plate cases investigated in a previous study. Moreover, the tip amplitude of the plates and the maximum strains were measured in order to find an optimum position for placing a piezoelectric polymer to harvest energy from the flow

Reduction of fluid forces and vortex shedding frequency of a circular cylinder using rigid splitter plates

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This study investigates the fluid forces acting on a circular cylinder in a laminar flow regime while using a passive control strategy. Three cases including the cylinder with one, two or three rigid splitter plates attached at its rear surface were considered and the location of horizontal plates (attachment angle) was varied between 0° and 90°. A comprehensive parametric study was performed to identify the optimum arrangement of the plates using the commercial finite element software, Comsol Multiphysics. The results show that the location and the number of the plates have crucial effects on the wake control. Increasing the number of splitter plates from one to two symmetric parallel plates led to a reduction in drag force, vortex shedding frequency and fluctuation of lift force. A maximum drag reduction of 23% for dual-splitters and 15% for single-splitter was achieved, at an angle of 45° at Reynolds number 100. However, increasing the number of attached plates to three didn’t have a significant effect on flow quantities when plates of the same length were utilised. The suitability of the third plate (the middle plate) was further studied by investigating the effect of length of the plate on flow quantities

Topology optimization of geometrically nonlinear structures using an evolutionary optimization method

Iso-XFEM method is an evolutionary optimization method developed in our previous studies to enable the generation of high resolution topology optimised designs suitable for additive manufacture. Conventional approaches for topology optimization require additional post-processing after optimization to generate a manufacturable topology with clearly defined smooth boundaries. Iso-XFEM aims to eliminate this time-consuming post-processing stage by defining the boundaries using isovalues of a structural performance criterion and an extended finite element method (XFEM) scheme. In this paper, the Iso-XFEM method is further developed to enable the topology optimization of geometrically nonlinear structures undergoing large deformations. This is achieved by implementing a total Lagrangian finite element formulation and defining a structural performance criterion appropriate for the objective function of the optimization problem. The Iso-XFEM solutions for geometrically nonlinear test-cases implementing linear and nonlinear modelling are compared, and the suitability of nonlinear modelling for the topology optimization of geometrically nonlinear structures is investigated

Evolutionary topology optimization using the extended finite element method and isolines

This study presents a new algorithm for structural topological optimization of two-dimensional continuum structures by combining the extended finite element method (X-FEM) with an evolutionary optimization algorithm. Taking advantage of an isoline design approach for boundary representation in a fixed grid domain, X-FEM can be implemented to improve the accuracy of finite element solutions on the boundary during the optimization process. Although this approach does not use any remeshing or moving mesh algorithms, final topologies have smooth and clearly defined boundaries which need no further interpretation. Numerical comparisons of the converged solutions with standard bi-directional evolutionary structural optimization solutions show the efficiency of the proposed method, and comparison with the converged solutions using MSC NASTRAN confirms the high accuracy of this method

Exploiting Generative Design for Multi-Material Inkjet 3D Printed Cell Instructive, Bacterial Biofilm Resistant Composites

As our understanding of disease grows, it is becoming established that treatment needs to be personalized and targeted to the needs of the individual. In this paper we show that multi-material inkjet-based 3D printing, when backed with generative design algorithms, can bring a step change in the personalization of medical devices. We take cell-instructive materials known for their resistance to bacterial biofilm formation and reformulate for multi-material inkjet-based 3D printing. Specimens with customizable mechanical moduli are obtained without loss of their cell-instructive properties. The manufacturing is coupled to a design algorithm that takes a user-specified deformation and computes the distribution of the materials needed to meet the target under given load constraints. Optimisation led to a voxel map file defining where different materials should be placed. Manufactured products were assessed against the mechanical and cell-instructive specifications and ultimately showed how multifunctional personalization emerges from generative design driven 3D printing

Exploiting Generative Design for 3D Printing of Bacterial Biofilm Resistant Composite Devices

open access articleAs the understanding of disease grows, so does the opportunity for personalization of therapies targeted to the needs of the individual. To bring about a step change in the personalization of medical devices it is shown that multi-material inkjet-based 3D printing can meet this demand by combining functional materials, voxelated manufacturing, and algorithmic design. In this paper composite structures designed with both controlled deformation and reduced biofilm formation are manufactured using two formulations that are deposited selectively and separately. The bacterial biofilm coverage of the resulting composites is reduced by up to 75% compared to commonly used silicone rubbers, without the need for incorporating bioactives. Meanwhile, the composites can be tuned to meet user defined mechanical performance with ±10% deviation. Device manufacture is coupled to finite element modelling and a genetic algorithm that takes the user-specified mechanical deformation and computes the distribution of materials needed to meet this under given load constraints through a generative design process. Manufactured products are assessed against the mechanical and bacterial cell-instructive specifications and illustrate how multifunctional personalization can be achieved using generative design driven multi-material inkjet based 3D printing

Insight into the mechanical properties of 3D printed strut-based lattice structures

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. This study was funded by the Faculty of Computing, Engineering and Media at De Montfort UniversitySince the development of additive manufacturing (3D printing), there has been a growing interest in the use of 3D printed lattice structures for a range of mechanical and biomedical applications. This study investigates the elastic properties of different types of strut-based lattice structures obtained through a series of compression tests and compares them against numerically calculated properties of intended designs. Two different 3D printing processes are employed for the fabrication of lattice structures, including selective laser sintering (SLS) and digital light processing (DLP). Gibson-Ashby power-law for cellular structures has been initially utilised as a framework for the comparison of numerical and experimental results. The results are normalised, allowing the comparison of elastic properties of lattices made in different polymer materials independent of the bulk material properties. This study suggests that although the mechanical properties of the fabricated parts are heavily dependent on the design of lattice unit-cell, the mechanical properties can be significantly different to those of intended designs depending on the 3D printing process used for the fabrication of lattice structures