| Solving the problem of large-scale elastic thin plate motion in a large area is one of the current hot demands.The elastic sheet has a wide range of engineering applications such as spacecraft,solar panels,rotating wings,and propeller blades.Taking the flexible body and biofilm with large deformable elastic thin plate structure as the background,the theory and method of rigid body dynamics are used to study the deformation and movement of the elastic thin plate.On this basis,the elastic thin plate is introduced into analytical mechanics,and then the analytical mechanics method is used.Study the modeling problem of large deformation elastic thin plates.First,under some basic assumptions,the "Kirchhoff dynamics comparison" is extended from the elastic thin rod mechanics to the elastic thin plate,so that the deformation and movement of the elastic thin plate corresponds to the rigid body mechanics in terms of physics concepts and is consistent in the expression of the mathematical formula;Cosserat direction,discussed the compatibility of the bending and twisting degree and derived the compatible relationship,expressed the strain and stress with the bending torsion,and derived the elastic partial equilibrium partial differential equation expressed by the internal force concentration.Considering the mid-line strain,the bending torsion is redefined and the bending torsion with the original arc coordinate as the independent variable is given.The strain,stress and constitutive relation of the unit body are expressed by the bending and twisting,and the elastic partial plate equilibrium partial differential equation expressed by the distributed internal force concentration is derived by using the post-deformation arc coordinate and the pre-deformation coordinate as independent variables.The elastic thin plate was introduced into analytical mechanics.Based on the analytical mechanics of the elastic bar’s arc coordinates,the elastic thin plate’s arc coordinate analysis mechanics was studied on the basis of dynamic comparison of the elastic thin plate.The equilibrium state of the elastic thin plate was analyzed using the principle of minimum potential energy of elasticity,and the elasticity was established.Based on the principle of sheet Hamilton,the Lagrange equation of arc coordinates is derived.Finally,the problems of analysis and modeling and numerical calculations of elastic thin plates with or with complex motion-big-deformation-growing are discussed. |
