*2.1. Structure and Grid*

According to the design method of diaphragm size of diaphragm valve, based on the nominal size DN20 series of diaphragm valve, the shape and size of diaphragm are preliminarily determined (Figure 1). The effects of the diaphragm thickness (*B*<sup>0</sup> = 4 mm, *B*<sup>0</sup> = 5 mm, *B*<sup>0</sup> = 6 mm) and the stem loading surface diameter on the diaphragm deformation were investigated.

**Figure 1.** Shape and size of the diaphragm with three kinds of the stem loading surface parameter.

The three-dimensional model of rubber diaphragm is imported into ANSYS static structure and meshed into model interface. Based on the mesh automatic meshing basic set value, the size function is selected adapted, and the relevance center selects course, and the mesh size is 1 mm. The hyper elastic material was selected as the model material. The neoprene rubber was extracted from ANSYS engineering data, and the density (ρ<sup>1</sup> = 1.25 g/cm3) and tensile strength (σ > 10 MPa) of the material were manually added. Figure 2a shows the model mesh with a diaphragm thickness of *B*<sup>0</sup> = 6 mm. The results show that the maximum skewness is 0.81, 0.81 and 0.82 under the three thicknesses, and the average is less than 0.5. The grid quality is good.

**Figure 2.** Numerical model of the diaphragm (**a**) the model mesh with a diaphragm thickness of *B*<sup>0</sup> = 6 mm and (**b**) the total deformation of the diaphragm with a thickness of *B*<sup>0</sup> = 4 mm.

Load setting (Table A1): Select large deformation in analysis setting, apply fixed load (flange of diaphragm upper and lower surface, simulate assembly fixing), standard gravity, uniform pressure (arc under diaphragm, simulate medium back pressure), fixed displacement (stem action plane, direction downward, *x*<sup>0</sup> = 15 mm, solve maximum deformation), and add no friction load (loading the side wall, limiting the deformation of the cylindrical surface). The resolver outputs the total displacement map, the longitudinal section displacement map and the longitudinal section stress map. Figure 2b shows the total deformation of the diaphragm with a thickness of *B*<sup>0</sup> = 4 mm.
