Using Topology Optimization & FDM 3D Printing to Make a Simply Supported Beam

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Many studies have been completed regarding the use of topology optimization to generate the best designs for 3D printed parts. A trio of researchers – Urvashi Verma, Vipin Gupta, and Jitendra Bhaskar – from the Mechanical Engineering department at Harcourt Butler Technical University (HBTU) Kanpur in India recently published their own paper, “Topological Optimization of Simply Supported Beam for Fused Deposition Modelling Process,” about combining 3D printing and topology optimization, and applying the results to a simply supported beam.

“Topology optimization can be described as a distribution of a given amount of material in a specified design domain, which is subjected to certain loading and boundary conditions. But these designs cannot be fabricated using conventional manufacturing technique but with the advent of 3D printing techniques complexity of design is no more a problem,” they wrote.

By combining these two technologies, you can get a tool to help create mechanical parts that have increased mechanical strength, while reducing material waste at the same time…no matter if the design is simple or complex.

The trio performed topology optimization on a simply supported beam, which was then 3D printed out of PLA material using fused deposition modeling (FDM) technology.

With the help of finite element analysis software from ANSYS, the researchers used the Solid Isotropic Material with Penalization, or SIMP, method to perform the topology optimization.

“The Solid Isotropic Material with Penalization method (SIMP) is the penalization scheme or the power law approach,” the researchers explained. “The SIMP method introduces the concept of material density as a non-physical, independent variable.

“The objective is to find an optimal material distribution in the design domain that subjected to some given constraints, leading to minimizing a specified objective function.”

They explained that “the stiffness of intermediate densities is penalized, so they are not favoured,” which results in a final design of only void and solid regions. The SIMP material model also helped the researchers “obtain a structure with maximum stiffness by minimizing compliance.”

The team chose a simply supported beam, with mid-point load, for their topology optimization research.

“Objective function is compliance, design variable is pseudo density and state variables are the response of structures that is deflection and von misses stresss. Objected function is subjected to volume constraint and by minimize the compliance, stiffness of beam is maximized. The total volume of the beam is considered as the design area and volume constraints is kept as 50%,” they wrote.

Boundary conditions for simply supported beam formulation

The figure above shows the boundary conditions for the beam, while the table provides its dimensions.

Displacement plot solution for simply supported beam

In order to see displacement and stress distribution, the team performed a finite element analysis. The contour plots above and below illustrate these measurements, respectively, for the beam’s load case.

Von misses stress distribution for simply supported beam

In the element density distribution plot below, red equals elements that have a density equal to one, which are the part’s load bearing elements. The large blue areas of the part are elements with a density equal to zero, which will likely “need material removal as they have negligible effect on the performance of the part and can be neglected from optimized design.”

Element density distribution plot for simply supported beam

The other colors (values) in the plot, such as green and yellow, represent the intermediate density, which is “penalized to obtain a practical design” with the SIMP method.

Due to their complexity, these topology optimized designs would be impossible to make using conventional methods of manufacturing, which is why FDM 3D printing was so useful – the technology is capable of making these types of complex shapes.

Topology optimized simply supported beam

“This paper shows an example of the capability of fused deposition modelling 3D printing process by using Topology optimization methods such as Solid Isotropic material with Penalization,” the researchers concluded.

FDM 3D printed topology optimized simply supported beam

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