An efficient 3D topology optimization code written in Matlab

This paper presents an efficient and compact Matlab code to solve three-dimensional topology optimization problems. The 169 lines comprising this code include finite element analysis, sensitivity analysis, density filter, optimality criterion optimizer, and display of results. The basic code solves minimum compliance problems. A systematic approach is presented to easily modify the definition of supports and external loads. The paper also includes instructions to define multiple load cases, active and passive elements, continuation strategy, synthesis of compliant mechanisms, and heat conduction problems, as well as the theoretical and numerical elements to implement general non-linear programming strategies such as SQP and MMA. The code is intended for students and newcomers in the topology optimization. The complete code is provided in Appendix C and it can be downloaded from http://​top3dapp.​com

Proportional Topology Optimization: A new non-gradient method for solving stress constrained and minimum compliance problems and its implementation in MATLAB

A new topology optimization method called the Proportional Topology Optimization (PTO) is presented. As a non-gradient method, PTO is simple to understand, easy to implement, and is also efficient and accurate at the same time. It is implemented into two MATLAB programs to solve the stress constrained and minimum compliance problems. Descriptions of the algorithm and computer programs are provided in detail. The method is applied to solve three numerical examples for both types of problems. The method shows comparable efficiency and accuracy with an existing gradient optimality criteria method. Also, the PTO stress constrained algorithm and minimum compliance algorithm are compared by feeding output from one algorithm to the other in an alternative manner, where the former yields lower maximum stress and volume fraction but higher compliance compared to the latter. Advantages and disadvantages of the proposed method and future works are discussed. The computer programs are self-contained and publicly shared in the website www.ptomethod.org.Comment: 18 pages, 8 figures, and 2 appendices (MATLAB codes

Coupled CFD Shape Optimization for aerodynamic profiles

The present document deals with the optimization of shape of aerodynamic profiles -- The objective is to reduce the drag coefficient on a given profile without penalising the lift coefficient -- A set of control points defining the geometry are passed and parameterized as a B-Spline curve -- These points are modified automatically by means of CFD analysis -- A given shape is defined by an user and a valid volumetric CFD domain is constructed from this planar data and a set of user-defined parameters -- The construction process involves the usage of 2D and 3D meshing algorithms that were coupled into own- code -- The volume of air surrounding the airfoil and mesh quality are also parametrically defined -- Some standard NACA profiles were used by obtaining first its control points in order to test the algorithm -- Navier-Stokes equations were solved for turbulent, steady-state ow of compressible uids using the k-epsilon model and SIMPLE algorithm -- In order to obtain data for the optimization process an utility to extract drag and lift data from the CFD simulation was added -- After a simulation is run drag and lift data are passed to the optimization process -- A gradient-based method using the steepest descent was implemented in order to define the magnitude and direction of the displacement of each control point -- The control points and other parameters defined as the design variables are iteratively modified in order to achieve an optimum -- Preliminary results on conceptual examples show a decrease in drag and a change in geometry that obeys to aerodynamic behavior principle

Metamodel-assisted design optimization of piezoelectric flex transducer for maximal bio-kinetic energy conversion

Energy Harvesting Devices (EHD) have been widely used to generate electrical power from the bio-kinetic energy of human body movement. A novel Piezoelectric Flex Transducer (PFT) based on the Cymbal device has been proposed by Daniels et al. (2013) for the purpose of energy harvesting. To further improve the efficiency of the device, optimal design of the PFT for maximum output power subject to stress and displacement constraints is carried out in this paper. Sequential Quadratic Programming (SQP) on metamodels generated with Genetic Programming from a 140-point optimal Latin hypercube design of experiments is used in the optimization. Finally, the optimal design is validated by finite element simulations. The simulations show that the magnitude of the electrical power generated from this optimal PFT harvesting device can be up to 6.5 mw when a safety design factor of 2.0 is applied

Flexural bending test of topology optimization additively manufactured parts

The aim of this work is to model, manufacture, and test an optimized Messerschmitt-BölkowBlohm beam using additive manufacturing. The implemented method is the Solid Isotropic Material with Penalization of a minimum compliance design. The Taubin smoothing technique was used to attenuate geometric noise and minimize the formation of overhanging angles and residual stresses due to the thermal activity of the selective laser melting process. The optimized model required examination and repair of local errors such as surface gaps, non-manifold vertices, and intersecting facets. A comparison between experimental and numerical results of the linear elastic regimes showed that the additively manufactured structure was less stiff than predicted. Potential contributors are discussed, including the formation of an anisotropic microstructure throughout the layer-by-layer melting process. In addition, the effect of selective laser melting process on the mechanical properties of stainless steel 316l-0407 and its influence on structural performance was described