Research On Method Of Solving Elastic-plastic Problem Based On Theory Of Duality Disturbance

Solving the problem of elastic-plastic with theory of elastic-plastic usually tracking the history of plastic deformation and use an incremental method for solving,but the solving process is more complex.For some engineering plastic mechanics problems,the efficiency of solving problem is a little low.Establishing a constitutive relation which mechanics concept is clear and is convenient to use is still an important topic for elastic-plastic mechanics.Theory of Duality Disturbance provides a new theoretical system which can simulate complex mechanical behavior(including elastic-plastic,reinforcement,softening and damage).It is important to establish an explicit relationship between disturbance and plastic strain.Based on Concept of Duality Disturbance,looking for a simple and effective method to solve the problem of elastic-plastic is a specific application of Theory of Duality Disturbance.The main work in this thesis has several aspects as following:(1)Based on test data,established a new stress-strain constitutive relationship,namely non-fitted nonlinear stress-strain constitutive equation.This equation is successfully applied to nonlinear beam bending.Nonlinear bending moment-curvature is based on plane section assumption.The calculating example shows that the nonlinear bending moment-curvature equation is considerably correct for nonlinear analysis of engineering beam.(2)Established a constitutive equation between disturbance and plastic strain,which put non-fitted nonlinear stress-strain relationship relatively disturbance status and put linear elastic relationship as complete disturbance status.This party predicted apparent stress-strain curve and test the apparent stress-strain curve are fit well.It shows that the disturbance and plastic strain constitutive equation is correct.(3)Based on Theory of Duality Disturbance,established a method of solving the problems of elastic-plastic strengthening.Using this method,the cantilever by bending and torsion deformation was analyzed.Examples show that the method can be very convenient and effective to solve the problems of elastic-plastic strengthening which satisfied Mises strength criterion.