# Investigation of Fluid-Structure Interaction Induced Bending for Elastic Flaps in a Cross Flow
## 1 Introduction  
Fluid-structure interaction (FSI) states the mutual interaction of a structure with a flowing fluid and develops the fluid and solid motions and the dependency of these motions on each other. Such kind of problems involve, the velocity and pressure of fluid effects and are affected by the structure deformation. In recent years, it has become a prominent characteristic of various engineering projects because design involves lighter and more flexible structures. The conduct of these structures with a fluid generates multi physical situations which are usually complex to handle. Numerical calculations play an important role in most engineering areas and have become more challenging due to the prediction of different flow regimes which cannot be seen in experiments (EXP) but it is still a challenge to have accurate numerical simulation of a FSI problem because of strong fluid-structure coupling. FSI problems are ever present in nature for example flapping wings, flags [1; 2; 3; 4; 5; 6; 7; 8; 9], aquatic animals [10], flexible vegetation [11; 12; 13], in hemodynamics [1; 14] and human hair and hair sensors [15]. Thin structures are of great interest for microfluidic procedures in engineering and biomedical applications [16; 17; 18] and structural dynamics [19; 20; 18]. For investigating fluid motion together with the structure, extensive theoretical, experimental and numerical studies across flexible plates are carried out in the context of plate flapping, vibration,flutter instability, the effect of wake on plate stability and the estimation of natural frequency for plates exposed to axial flow directions [21; 22; 23; 24; 25]. Results indicate that the flapping amplitude of the plate is mainly controlled by the elastic modulus and density ratio whereas frequency is a function of length-thickness ratio and density ratio. Also with an increase in Reynolds number, the plate indicates the transfer of symmetric to asymmetric flapping [21]. The forcing amplitude is the major influence on the plate resonance while flow velocity and plate bending rigidity indicate only the minor effect providing the forcing frequency is normalized with the natural frequency of the plate [10]. Aside from flat plates in axial flow direction, research work is offered to examine a vertical bottom-fixed flat plate in a laminar boundary layer. A study representing the Reynolds number, structure-to-fluid mass ratio and bending of the plate, respectively, determine the dynamic behavior of the flexible plate. Based on this, a two-dimensional (2D) numerical study [26] presents the dynamic response of a flexible plate engrossed in laminar condition for Reynolds numbers of \(100,200,400\) and \(800\) by an immersed boundary method (IBM). The dynamics of the plate indicate that the plate is stable for a low Reynolds number; however, when the Reynolds number reaches \(800\), the plate starts vibrating. The effect of bending rigidity, ranging from \(0.1\)-\(1.6\), demonstrates the periodic vibrations of the plate at low values and chaotic vibration when bending rigidity approaches between \(0.2\) and \(0.4\), then switching to periodic vibration again for a bending rigidity of \(0.8\) and \(1.6\). In comparison with the flapping flag [27], the plate shows a considerably different response in terms of frequency and vibrations. The interaction of severely deformed structures with their environment is significant in many life science applications and technical systems. Nevertheless, precise and stable numerical methods for illustrating such problems are still exceptional. [PERSON] et al. [28] developed a coupling between an existing immersed boundary flow solver together with a nonlinear finite element (FE) solver. Furthermore, they evaluate six practical applications of FSI specifically for three dimensions (3D), which primarily have large deformations.