Small deflection calculation and analysis of circular thin plate under different constraints12151kloc-0/96 background In the course of material mechanics, the main content of chapter 7 is the bending deformation of beams. Through the finite element analysis of the beam, the formulas of small deflection of the beam under different constraints and different forces are derived. But in practical engineering applications, there is another common situation-the stress of thin plates, which is not discussed in the book. This paper will calculate and analyze a special case of small deflection, that is, a circular thin plate under uniform load. Modeling, calculation and analysis 2. The stress model of1circular thin plate and its basic assumptions, consulting relevant materials and combining with book knowledge, first discuss the situation of lateral symmetry of uniformly distributed load, and make the following basic deformation assumptions: when the plate is bent, its middle plane remains neutral, that is, all points in the middle plane do not undergo expansion and shear deformation, and only the points located on the neutral surface normal line before deformation along the middle plane remain on the same normal line of the elastic surface after deformation, between points on the normal line. The layers of materials parallel to neutral surface do not squeeze each other, that is, the normal stress in the plate perpendicular to the plate surface is very small and can be ignored. Based on this, the small deflection bending differential equation of circular thin plate subjected to axisymmetric transverse load can be derived by finite element method: the transverse shear force at the distance r from the center of the circle is d, where h is the thickness of circular thin plate and μ is Poisson's ratio of material. 2.2 Calculation of internal force and deflection and rotation equation of circular thin plate Add a uniformly distributed load with concentrated force q to circular thin plate, as shown in the figure. Then it is obtained by integrating the variable r in the above formula for three consecutive times. Since W at r=0 should be a finite value, there should be C2=0. Finally, C 1 and C3 should be determined by boundary adjustment. Calculation under several different constraints 3. 1 The circumference is a fixed support. Because the circumference is a fixed bearing, deflection and rotation angle are not allowed, so there is a boundary condition 64. Therefore, the equations of rotation angle and deflection of fixed bearing with circumference are: 3.2 The circumference is a simple bearing (unconstrained rotation angle). At this time, there is a constraint: 3.3 The center of the circle is a fixed or simple bearing. If it is a fixed bearing, there is a constraint at this time: in the case of simply supported periphery, the rotation angle is not limited at the periphery, just like in the case of constraint at the center. Then, when these two central constraints can be obtained, the values of deflection and rotation angle equations are opposite to those in 3.2. The deflection of circular thin plate under uniform load under different constraints is analyzed and summarized. 4. 1 Because the constraint at the center can be equivalent to a simply supported constraint at the periphery, this part only discusses the deflection of the first two constraints. When the bearing is fixed, the maximum deflection is in the center, which is 64. When the bearing is simple, the maximum deflection is in the center, which is 644.2. The results show that the maximum deflection when the bearing is fixed is less than that when the bearing is simple, so to reduce the deformation, the constraint form of fixed bearing should be adopted, and the constraint between fixed and simple is generally adopted in engineering. When the material and load of the plate are determined, reducing the radius and increasing the thickness of the plate can reduce the deflection, thus reducing the deformation. 4.3 Summary By consulting relevant literature, the relevant formulas for calculating the deflection of circular thin plates under uniformly distributed load are obtained, and then the formulas for calculating the deflection under two simple constraints are obtained. However, due to the different constraint strength of the model, the deflection calculation formula of simply supported bearing is different from the results in the data, but the error is not big, and a good conclusion can be obtained in a certain range.