Exact solution of the nonlinear boundary value problem for the basic equation and boundary condition of circular membrane under central force was obtained by using new simple methods. The existence and uniqueness of t...Exact solution of the nonlinear boundary value problem for the basic equation and boundary condition of circular membrane under central force was obtained by using new simple methods. The existence and uniqueness of the solution were discussed by using of modern immovable point theorems. Although specific problem is treated, the basic principles of the methods can be applied to a considerable variety of nonlinear problems.展开更多
The analytical solution to a Foppl-Hencky membrane with a rigidly clamped boundary condition under concentrated force is provided. Stability of a nonlinear circular membrane is investigated.
Elastomeric membranes are frequently used in several emerging fields such as soft robotics and flexible electronics.For convenience of the structural design,it is very attractive to find simple analytical solutions to...Elastomeric membranes are frequently used in several emerging fields such as soft robotics and flexible electronics.For convenience of the structural design,it is very attractive to find simple analytical solutions to well describe their elastic deformations in response to external loadings.However,both the material/geometrical nonlinearity and the deformation inhomogeneity due to boundary constraints make it much challenging to get an exact analytical solution.In this paper,we focus on the inflation of a prestretched elastomeric circular membrane under uniform pressure,and derive an approximate analytical solution of the pressure-volume curve based upon a reasonable assumption on the shape of the inflated membrane.Such an explicit expression enables us to quantitatively design the material and geometrical parameters of the pre-stretched membrane to generate a target pressure-volume curve with prescribed peak point and initial slope.This work would be of help in the simplified mechanical design of structures involving elastomeric membranes.展开更多
文摘Exact solution of the nonlinear boundary value problem for the basic equation and boundary condition of circular membrane under central force was obtained by using new simple methods. The existence and uniqueness of the solution were discussed by using of modern immovable point theorems. Although specific problem is treated, the basic principles of the methods can be applied to a considerable variety of nonlinear problems.
文摘The analytical solution to a Foppl-Hencky membrane with a rigidly clamped boundary condition under concentrated force is provided. Stability of a nonlinear circular membrane is investigated.
基金Supports from the National Natural Science Foundation of China (Grants 11772272 and 11972027)the support from the Fundamental Research Funds for the Central Universities (Grants 2682019LK06 and 2682019LXCGKY001)
文摘Elastomeric membranes are frequently used in several emerging fields such as soft robotics and flexible electronics.For convenience of the structural design,it is very attractive to find simple analytical solutions to well describe their elastic deformations in response to external loadings.However,both the material/geometrical nonlinearity and the deformation inhomogeneity due to boundary constraints make it much challenging to get an exact analytical solution.In this paper,we focus on the inflation of a prestretched elastomeric circular membrane under uniform pressure,and derive an approximate analytical solution of the pressure-volume curve based upon a reasonable assumption on the shape of the inflated membrane.Such an explicit expression enables us to quantitatively design the material and geometrical parameters of the pre-stretched membrane to generate a target pressure-volume curve with prescribed peak point and initial slope.This work would be of help in the simplified mechanical design of structures involving elastomeric membranes.
