Proceedings of the 2018 Canadian Society for Mechanical Engineering (CSME) International Congress

Published proceedings of the 2018 Canadian Society for Mechanical Engineering (CSME) International Congress, hosted by York University, 27-30 May 2018

Revisiting Non-Convexity in Topology Optimization of Compliance Minimization Problems

Purpose: This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. We trace the different sources of non-convexification in the context of topology optimization problems starting from domain discretization, passing through penalization for discreteness and effects of filtering methods, and end with a note on continuation methods. Design/Methodology/Approach: Starting from the global optimum of the compliance minimization problem, we employ analytical tools to investigate how intermediate density penalization affects the convexity of the problem, the potential penalization-like effects of various filtering techniques, how continuation methods can be used to approach the global optimum, and how the initial guess has some weight in determining the final optimum. Findings: The non-convexification effects of the penalization of intermediate density elements simply overshadows any other type of non-convexification introduced into the problem, mainly due to its severity and locality. Continuation methods are strongly recommended to overcome the problem of local minima, albeit its step and convergence criteria are left to the user depending on the type of application. Originality/Value: In this article, we present a comprehensive treatment of the sources of non-convexity in density-based topology optimization problems, with a focus on linear elastic compliance minimization. We put special emphasis on the potential penalization-like effects of various filtering techniques through a detailed mathematical treatment

Preparing and Coordinating Undergraduate Engineering Design Projects

Paper presented at 2018 Canadian Society of Mechanical Engineers International Congress, 27-30 May 2018.Design projects have become common in engineering classrooms. Earlier exposure to and training in the design engineering process hold much value for an enriched experience and an in-depth understanding of engineering design. Simultaneously, students in their earlier years require more guidance and frequent feedback to inform their own expectations of learning objectives, as well as develop effective learning strategies. In this paper, we will examine the considerations required to design and conduct an undergraduate engineering design course, with reflections from several years’ experience with a second-year mechanical engineering design course

The Effect Of High Strain Rate On The Piezo-Resistance Of Polydimethylsiloxane With Carbon Nanotubes

This paper describes the piezoresistive properties of a nanocomposite made of polydimethylsiloxane and multi- walled carbon nanotubes that is subjected to high strain rate. We highlight the production process of the composite, the testing protocol, and the results obtained

Material Properties Of 3D Printed Parts: Challenges In Design And Analysis

The present paper addresses the challenges in design and analysis of 3D printed structures with anisotropic material properties. In recent years the additive manufacturing technologies have been used in most of the industries because of their freedom in fabrication of any complex geometry part. However, the final properties of the 3D printed parts are anisotropic though the material used is isotropic. Further, the properties of printed part are not homogeneous. This change in the properties is due to process parameters and build orientation of the parts. Therefore, this calls special attention of the designer for effective design and analysis of such parts. In this paper, design consideration of the parts for 3D printing and also, their structural analysis for effective design of parts for 3D printing are discussed. Further, different steps involved from design to 3D printing of a product are discussed

Direction-Oriented Stress-Constrained Topology Optimization of Orthotropic Materials

Efficient optimization of topology and raster angle has shown unprecedented enhancements in the mechanical properties of 3D printed materials. Topology optimization helps reduce the waste of raw material in the fabrication of 3D printed parts, thus decreasing production costs associated with manufacturing lighter structures. Fiber orientation plays an important role in increasing the stiffness of a structure. This paper develops and tests a new method for handling stress constraints in topology and fiber orientation optimization of 3D printed orthotropic structures. The stress constraints are coupled with an objective function that maximizes stiffness. This is accomplished by using the modified solid isotropic material with penalization method with the method of moving asymptotes as the mathematical optimizer. Each element has a fictitious density and an angle as the main design variables. To reduce the number of stress constraints and thus the computational cost, a new clustering strategy is employed in which the highest stresses in the principal material coordinates are grouped separately into two clusters using an adjusted $P$-norm. A detailed description of the formulation and sensitivity analysis is discussed. While we present an analysis of 2D structures in the numerical examples section, the method can also be used for 3D structures, as the formulation is generic. Our results show that this method can produce efficient structures suitable for 3D printing while thresholding the stresses

High Strain-Rate Behavior Of Mechanoluminescent Material Dispersed In A Soft Polymer Matrix

Mechanoluminescence (ML) is the emission of light from a solid material in response to mechanical stimuli [1]. Mechanoluminescent materials are classified based on the types of stress activation required for luminescence behaviour. In this paper, we propose the study of light emission characteristics of an elastico-mechanoluminescent (EML) material dispersed in a soft polymer matrix, under high-strain compressive loading for a qualitative and quantitative testing of onsite strain. We developed a strain sensor by creating a composite material through the combination of a polydimethylsiloxane (PDMS) matrix structure and strontium aluminate, europium, and dysprosium doped (SAOED) crystals. SAOED crystals possess a strong luminescence behavior, which has led to their proliferation as a viable optical sensor. Composite materials were tested using a modified Kolsky bar and high-speed camera. The light-emitting characteristics of the SAOED crystals in response to mechanical stimuli allows for the quantification of stress–strain experienced by the composite material. The light intensity, which is measured by a complementary metal–oxide–semiconductor (CMOS) sensor in a high-speed digital camera, provides a quantitative measure of the strain-rate. Light-emitting characteristics of the EML material and the strain behavior of the material were studied

Collapse Surfaces Of The Octet-Truss Lattice At Different Lattice Angles

Cellular materials are found extensively in nature such as wood, honeycomb, butterfly wings and foam-like structures like trabecular bone and sponge. This class of materials proves to be structurally-efficient by combining low weight with superior mechanical properties. Recent studies have shown there are coupling relations between the mechanical properties of cellular materials and their relative density. Due to its favorable stretching‐dominated behavior, continuum models of the octet‐truss were developed to describe its effective mechanical properties. However, previous studies were only performed for the cubic symmetry case where the lattice angle �=45°. In this work, we study the impact of the lattice angle on the effective strength of the octet-truss. A graphical method is utilized to plot the collapse surfaces for plastic yielding and elastic buckling for different loading combinations at different lattice angles. Generally, the (�̅��,�̅��) loading space is preferable for lattice angles greater than 45°, while the (�̅��,�̅��) loading space is preferable for lattice angles lower than 45°

Penalization in Density-Based Topology Optimization: A Mathematical Perspective

Most real-life engineering optimization problems are non-convex by nature. In a topology optimization context, this non-convexity is even exacerbated by the extra restrictions imposed during the optimization process to enforce mesh-independent black/white manufacturable solutions. Such restrictions include intermediate density penalization, as well as external regulation techniques imposed to tackle some numerical instabilities such as checkerboarding and mesh dependence, in addition to various design constraints. This non-convexity gives rise to the problem of local minima, where the converged solution is greatly affected by the algorithmic parameters as well as the initial guess. To overcome this non-convexity, it's often advised to use continuation methods, that is to introduce non-convexification gradually between iterations. In this article, we present a comprehensive treatment of the sources of nonconvexity in density-based topology optimization problems, with a special emphasis on linear elastic compliance minimization. This is in an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic

A Novel Finite Strain Visco-Hyperelasticity Based Constitutive Model For Elastomers

A novel three-dimensional finite strain viscohyperelastic constitutive model is proposed to capture the strain rate dependency of rubber-like materials. The overall material behavior is defined by cumulative description of hyperelasticity and nonlinear viscoelasticity. The hyperelastic part is based on exponential logarithmic Hart-Smith strain energy function and the viscous part comprises of a fading integral which links the current stresses to the applied strain history. The derived analytical framework is verified with respect to experimental data. The potential of the proposed model has been constituted by an excellent fit between proposed model and considered test data