Analysis Model Of Laminated Micro-beam/plate Structure For Improving The Prediction Accuracy Of Interlaminar Stress

Laminated microbeam/plate sturctures have the advantages of high performance,versatility,and good designability,and are widely used in microelectromechanical systems(MEMS).Due to the relatively weak mechanical properties at the interface between layers,delamination failure has become an important failure mode for laminated microbeam/plate structures.The accurate prediction of the interlaminar stress of the laminated microbeam/plate structure is a prerequisite for the accurate evaluation of its delamination failure.Therefore,the establishment of an analysis model of the laminated microbeam/plate structure and the accurate prediction of the interlaminar stress of the laminated microbeam/plate structure have important scientific significance and engineering practical value.The accurate prediction of the interlaminar stress depends on the proposal of high-precision lamination theory,the selection of more suitable constitutive relations and the construction of more accurate calculation methods of the interlaminar stress.In order to obtain a more accurate lamination theory,a highprecision third-order zigzag theory that can satisfy the continuous interlaminar stress in advance is established in this paper.Aiming at the phenomenon that micro-scale structures have size effects,the laminated microbeams/plates are regarded as microstructures composed of coupled stress media.A simplified model of laminated microplates based on the coupled stress theory is constructed.In order to further improve the prediction accuracy of the interlaminar stress of the laminated microbeam/plate structure,a high-precision calculation method of the transverse shear stress is constructed based on the equivalent method of shearing virtual strain energy.Based on the above research,a zigzag model of the laminated microbeam/microplate that consideers the size effect and can satisfy the continuous interlaminar stress in advance is finally established,which can realize the accurate prediction of the interlaminar shear stress of laminated microbeam/plate structure.The main research content and results are as follows.(1)Calculation method of transverse shear stress based on equivalent shear virtual strain energy and its C0 element.In order to solve the problem of calculating the high-order derivatives of displacement parameters and constructing higher-order elements in the transverse shear stress calculation method(TCM)of the three-dimensional balance equation,a new transverse shear stress calculation method(NCM)was established.This NCM eliminates the high-order derivatives of displacement parameters in TCM based on equivalent shear virtual strain energy.Based on the NCM,the interlaminar shear stress of laminated beams/plates can be accurately predicted using only low-order elements.Based on the proposed NCM and the zigzag theories,a C0 continuous two-node linear beam element and a C0 continuous four-node quadrilateral linear plate element are constructed.Numerical examples show that the proposed linear elements can accurately predict the transverse shear stress of laminated beams/plates,which proves the effectiveness of the NCM.In addition,the feasibility of combining the NCM with plate/shell elements in commercial software to predict the transverse shear stress of the laminated structure is also explored.(2)Third-order zigzag beam theory satisfying the interlaminar stress continuity in advance and its beam element.Aiming at the problem of insufficient precision of the existing zigzag theories to predict the interlaminar stress of asymmetric or abrupt cross-section laminated structures,a new zigzag function that can accurately simulate the local distortion of the asymmetric laminated structure and describe the sudden change of the cross section of the laminated structure is constructed by a linear interpolation strategy of the interface displacement along the thickness direction.Based on the proposed zigzag function and the global third-order shear deformation theory,a third-order zigzag theory which satisfies the continuous interlaminar stress in advance is proposed.It has the same number of unknown variables as the global third-order shear deformation theory.In order to further improve the prediction accuracy of transverse shear stress,the NCM and the pre-processing method of transverse shear stress based on the Ressiner mixed variational principle are used.Based on the proposed third-order zigzag theory,using subparametric interpolation strategy,a C0 continuous two-node beam element without shear lock is constructed.By analyzing the static bending problems of asymmetric laminated beams and partially laminated laminated beams,the ability of the proposed three-order zigzag theory and beam element to predict the interlaminar stress of asymmetric laminated beams and laminated beams with abrupt cross-section is fully proved.(3)Simplified model of laminated microplate based on the couple stress theory.In order to solve the problems of the difficulty of constructing the couple stress plate element and the excessive number of degrees of freedom of the couple stress element,a simplified model of the laminated microplate based on the couple stress theory is proposed.Firstly,the influence of different geometrical parameters and material parameters on the accuracy of the traditional laminated microplate simplified model(SM)is studied by analytical method and finite element method,and the application scope of the SM is given for the first time.The SM is not suitable for the prediction of highly anisotropic or thick laminated microplates,nor for the prediction of higher-order modes.In order to overcome the shortcomings of the SM,a new simplified model(NSM)for laminated microplates based on the couple stress theory is proposed by ignoring the rotation angle of the out-of-plane direction.By comparing and studying the static bending,free vibration and buckling of laminated microplates,the calculation accuracy of the proposed NSM is verified.The numerical results show that the maximum error of the proposed NSM is only 1.4%,while the maximum error of the SM is up to 36.6%.In addition,the NSM also retains the advantages of high calculation efficiency of the SM.(4)The zigzag models of laminated microbeam/microplate with the continuous interlaminar stress and its couple stress elements.Aiming at the problem that the existing laminated microbeam/microplate models cannot accurately predict the interlaminar shear stress of the multilayer microbeams/microplates,laminated microbeam/plate zigzag models that consider the size effect and satisfy the interlaminar stress continuity in advance are established based on the proposed third-order zigzag theory and the NSM for the first time.In order to obtain more accurate transverse shear stress without increasing the difficulty of element construction,the proposed NCM is used again.Based on the proposed zigzag models and NCM,a two-node coupled stress beam element and a three-node triangular coupled stress plate element are constructed respectively.By analyzing the static bending problem of laminated microbeams/microplates,the ability of the proposed couple stress elements to predict the interlaminar shear stress of laminated microbeams/microplates is demonstrated.In addition,it also discusses the influence of the often-ignored couple stress term on the calculation accuracy of the transverse shear stress from the three-dimensional equilibrium equation.The numerical results show that the coupe stress term cannot be ignored when analyzing thick laminatedmicrobeams/microplates.