Several Micro Plate And Beam Models Based On Modified Couple Stress Theory

With the material size scaling down to the order of micro/nano-scales,the stiffness and the strength of metal materials can increase with the size decreasing.This phenomenon is commonly referred to as scale effects which can not be explained by conventional continuum theory due to lack of characteristic length parameters.However,couple stress theory can describe these effects phenomenologically by introducing length scale parameters.Therefore,it is very significant for us to make further study on the scale effect considering the theory problem and engineering appliance.For this purpose,several micro beam and plate models are developed based on modified couple stress theories to investigate the scale effects of their mechanical behaviors.Studies in the thesis can be concluded as follows:1.Several micro beam models are developed based on the isotropic couple stress theory proposed by Yang.Firstly,a model of micro axially functionally graded beam with arbitrary boundary conditions is proposed.And a strategy of reducing modulus is proposed to solve the bending problems of micro axially functionally graded beams only with classical beam elements.Sencondly,a free vibration model of micro non-uniform Reddy beam is developed in conjunction with the high order shear deformation theory.The scale effects in the free vibration of non-uniform micro beams and the effect of transverse shear deformation on the natural frequencies are investigated.2.Several micro composite laminated plate models are developed based on a new anisotropic couple stress theory proposed by Chen.Firstly,a free vibration model of composite laminated Reddy plate is developed.A simple supported plate is taken to be the illustrative example and analytical solved,the influence of the scale effects on the natural frequencies with different material length scale parameter is analyzed.The difference between the results obtained by different laminate theories is also discussed.Sencondly,a model of micro Reddy plate with complex boundary conditions is proposed based on finite element theory.The effects of ply orientation,boundary conditions and length-to-thickness ratio on natural frequencies of micro-scale composite laminated plates are studied.Thirdly,a model for angle-ply laminate plate is developed.The effect of the ply orientation on the scale effects are discussed.Finally,a new micro scale composite laminated plate model is proposed without any simplification by which the free vibration analysis is performed.Moreover,sevaral numerical examples are carried out to discuss the effects of simplify hypotheses on the natural frequencies of micro scale composite laminated plates and its scope application.