# Topology and Response Surface Optimization of a Bicycle Crank Arm with Multiple Load Cases
## 1 Introduction  
Since the oil and energy consumption issues have been rapidly arising during past decades, a non-fuel based vehicle such as the bicycle has been shifting people's preference. From the bike-to-work campaign up to the behavioral psychology study of the cyclist [1], cycling has apparently been part of people's common lifestyle ever since the 1900s. From the environmental side, cycling is also one of the best solutions to reduce the global warming issue. Recently, the South Korean government has initiated an effort to slash the greenhouse emissions by enforcing cycling as a transportation method instead of driving a car or motorcycle, as reported by The Korea Transport Institute (KOTI) [2]. This makes the bicycle become a more interesting topic for scientists, researchers, and even an international standardization body such as the International Standard Organization (ISO) [3]. One of the most important aspects that make a bicycle interesting for people, is the bicycle design. A design, besides being a matter of aesthetics, relates closely to the ergonomic of mechanical structure and even structural reliability [4; 5]. A good design will not only make human-machine interaction become better but also makes the machine itself more reliable and have a longer period of usage. A lightweight structure has been one of the biggest long-time challenges in the structural engineering industry since it relates closely to the structural performance, reliability, as well as manufacturing cost. This lighter structure has also made the bicycle design evolve since the pastyears. Bicycle manufacturers compete with each other to find a better production process and use several optimization methods to create lighter products without losing their performance. For instance, in the world of racing bikes, a lighter material means a big opportunity to reach faster speed in the competition. That is why several researchers have published their ideas to optimize and create a better bicycle component, i.e., the crank arm and pedal, as shown by several published patents [6; 7; 8]. Topology optimization is a well-known method in the design optimization process as has been discussed by researchers in terms of pursuing a lightweight structure [9]. It is a very powerful method to reduce the weight of a component without losing its best performance. [PERSON] et al. [10] investigate the stress-constrained topology optimization based on maximum stress measures that give beneficial information about an easy implementation, low computational cost, and stable converge topology optimization process. [PERSON] et al. [11] use multi-objective structural topology optimization for turbine brake pads subject to thermal and brake vibration. The result of the study shows that the optimized structure meets the stiffness requirement, as well as improves vibration performance. In a similar application, the same method has also been used to optimize the bucket foundation design of offshore wind turbines [12]. [PERSON] and [PERSON] [13] manage to optimize the weight of gearbox housing elements using topology optimization techniques. It provides potential directions for further gearbox housing development, as well. Topology optimization has also been used for improving spacecraft design for years. A study by [PERSON] et al. [14] utilize additive manufacturing and topology optimization to develop space flight hardware. The additive manufacturing constraints include the minimization of support structures and heat transfer jumps that can cause artifact warpage. The result shows that the proposed new optimized model is suitable for the respective missions. Meanwhile, [PERSON] et al. [15] implement a multi-objective topology optimization for a large-aperture space mirror. The optimized design is found to be very effective as a lightweight primary mirror assembly. In other applications, [PERSON] and [PERSON] [16] apply a topology optimization method using multi-objective population-based incremental learning and multigrid ground element.