## 1 Introduction  
Rice is the staple crop and plays an important role in China's agricultural production. According to statistical data of 2016, released by the Editorial Board of the Year Book of Agricultural Mechanization in China, China's rice yield reached 207,075.1 kt, the sown area 30,178.24 khm\({}^{2}\), and the mechanized harvesting rate was 87.11%. At present, many colleges, universities, and research institutions around the world focus on the intellectualization of rice harvesters; that is, achievement of automatic sensing and adjustment, and the adaptive control of different components on harvesters by utilizing different kinds of sensors. However, little work about the interaction between rice plant and harvesters has been done [1; 2; 3; 4; 5]. The deflection deformation of the rice plant, caused by reel, is important to determine a reasonable cutting height. For example, it is usually adopted by harvester operators to lift the header to a higher position during regular rice harvesting, to lower energy consumption in the processes of cutting, threshing, and cleaning. It is also required to harvest the main season of ratoon rice at a specific height to ensure the yield of ratoon season. In short, a proper cutting position could optimize the power configuration of harvesters and satisfy the requirement of special crop. As no accurate calculation methods exist for rice stalk deformation, the cutting height is simply decided empirically by operators. Thus, a simple and efficient calculation method of the deflection is needed. Parameters indispensable in the deflection calculation of crop stalks are Young's modulus and the cross-section moment of inertia, and many experiments have been conducted to acquire the parameters. [PERSON] et al. (2007) indicated that the elastic modulus of rice stalks increased as the stalk grew more mature, and the elastic modulus of the different internodes in the same variety varied, with the order being internode 2 \(>\) internode 3 \(>\) internode 4 [7]. A bending model of rice stalks based on formula deduction and empirical data was deduced in previous papers [8; 9]. [PERSON] et al. (2004) established a reel model in the lab to test the displacement response of rice and wheat stalks at the condition of quasi-state loading [10]. It was indicated that the rape stem of the elastic modulus increases with the reduction of moisture content of stem [11]. [PERSON] et al. (2005) reported that the modulus of elasticity of sunflower stalks decreased with increases in moisture content and stalk diameter [12]. [PERSON] et al. (2009) revealed that moisture content had a significant effect (\(p<0.05\)) on the modulus of elasticity of wheat stem of Alvand variety [13]. [PERSON] and [PERSON] (1999) found that the modulus of elasticity of sorghum stalk in bending did not change significantly (\(p<0.05\)) when the rate of loading was increased from 10 to 100 mm/min [14]. Accurate calculation of crop stalk deformation needs efficient algorithms which can be operated on an upper computer. [PERSON] et al. (2013) established an accurate lodging resistance model by applying an added approximate equation of deflection curve and principle of resident potential energy [15]. [PERSON] et al. (1998) also introduced the large deflection formula into the deflection calculation, but the calculation process was complicated and time-consuming [16]. [PERSON] et al. (1998) deduced the formula for cantilever beam with variational cross-section subject to pure bending in large deflection [17]. [PERSON] (2003) used the boundary integral method to solve the problem of bending of the heavy camber cantilever beam [18]. [PERSON] and [PERSON] (1998) introduced the numerical integral method to solve the deformation of large deflection bending of the cantilever beam [19]. The primary objective of this study was to develop an easy, quick, and accurate numerical calculation method to achieve the calculation of the deflection curve of rice stalks to provide a basis for establishing a complete rice plant deformation model.