Session: 08-12-01: Optimization, Uncertainty and Probability

Paper Number: 167227

Modal Topology Optimization 

Topology optimization has been a tool within commercial finite element method (FEM) codes that allows optimization of the geometry of new designs. An example of this method is to use the strain energy of the structure under load to decide which elements of the original domain can be subtracted to form a new lighter structure, still capable of taking the specified loading without exceeding the yield strength (maintaining mechanical strength).

There are several other ways to implement topology optimization such as element-based methods that include the solid isotropic microstructure with penalization (SIMP), the rational approximation of material properties (RAMP), the optimal microstructure with penalization (OMP), the non-optimal microstructure (NOM), and the dual discrete programming (DDP). There are discrete methods. Other methods can be classified as discrete methods such as the evolutionary structural optimization method (ESO), the additive optimization method (AESO) and the bidirectional evolutionary structural optimization method (BESO). These are just a few of the topology optimization methods that can be found in the literature. All the methods above are supported by a formal algorithm and could be considered mathematically intense.

This work presents a method to select the elements that are more likely to work against the load selecting the elements from a single mode of vibration. The main disadvantage of the method may be the identification of the mode of vibration that could be used as the based of the topology optimization. This mode of vibration must have limited displacement in the loading areas. The second problem to be solved is the selection of the elements with larger displacements in the mode that are better candidates to be deleted from the domain of the new design. Three different examples are presented. The FEA code Abaqus is used to produce the topology optimization measuring the strain energy and it is used for comparison with the proposed method in this work. The first example is a cantilever plate modelled with shell elements with an in-plane load, the second example is a hollowed bracket constrained at its based with a load perpendicular to its base applied on its the “free side.”  The bracket is modelled with tetrahedra elements. It is shown that if the loads, geometry and modes of vibration are known, it may be possible to produce a structural light and sound structure if the appropriate mode of vibration is selected as the basis of the structure. This may also result in a faster solution.

Presenting Author: Luis Monterrubio Robert Morris University

Presenting Author Biography: Luis Monterrubio, Ph.D., CMfgE
Associate Professor of Mechanical Engineering

Luis Monterrubio joined the Robert Morris University Engineering Department as an Assistant Professor in the Fall of 2013. He earned B.Eng. from the Universidad Nacional Autónoma de México, a M.A.Sc. from the University of Victoria, Canada and his Ph.D. from the University of Waikato, New Zealand. All degrees are in Mechanical Engineering and both M.A.Sc. and Ph.D. studies are related with vibrations. After his Ph.D. he worked at the University of California, San Diego as postdoctoral fellow in the area of bioacoustics. He teaches dynamics; machine design; numerical methods; finite element method; systems dynamics and control; and the capstone project course. His research interests are in vibration; numerical methods; finite element methods; continuum mechanics; acoustics; and engineering education. He has worked for the automotive industry in drafting, manufacturing, testing (internal combustion engines –vibration, fatigue, thermo-shock, tensile tests, power, torque and exhaust emissions, etc.), simulations (finite element method) and as a project manager (planning and installation of new testing facilities). He is a member of the American Society of Mechanical Engineers and the Society of Manufacturing Engineers.

Authors:

Luis Monterrubio Robert Morris University