High-performance Global-local Higher-order Theory And Higher-order Laminated Plate Elements

Aim of this thesis is to propose more accurate and efficient laminated plate theories afterobjectively estimating previous the displacement-based laminated plate theories. To pursuethis goal, this thesis firstly compared several theories by using analytical methods. Numericalresults show that 1,2-3 global-local higher-order theory is able to accurately predict transverseshear stresses without any smoothing methods as the number of layers of laminated plates isless than five. Based on this theory, several laminated plate elements have been constructed.Moreover, these elements were used to analyze bending, vibration and buckling of laminatedplates. By further research on 1,2-3 global-local higher-order theory, it is found that thistheory will encounter some accuracy difficulties to analyze bending of multilayered plates andthermal expansion of laminated plates. In view of computational efficiency and range ofapplicability, this thesis proposes several enhanced global-local higher-order theories andstudies detailedly laminated plate elements. Main work includes the following aspect:1. Proposed several global-local higher-order theories.●To improve computional efficiency, Reddy-type global-local higher-order theory ispresented. This theory can a priori satisfy continuity of in-plane displacements andtransverse shear stresses at interfaces. Moreover, compared to 1,2-3 global-localhigher-order theory, number of independent variables is reduced to 7. This theory hasbeen used to analyze bending of lamianted plates with few layers and functionally gradedplates.●By increasing the number of orders of the global in-plane displacement component in1,2-3 global-local higher-order theory, the global-local higher-order theory GLHT-m0 ispresented. Using this theory, effects of higher-order global-local shear deformations onbending, vibration and buckling of multilayered plates have been studied and thecorresponding conclusions are drawn: considering computational efficiency and accuracyof the results, the fifth-order global-local theory (m=5) should be applied to predict thestatic, the dynamic and the buckling response of multilayered plates.●For thermal expansion problems of laminated plates, transverse normal strain plays animportant role. To analyze such problems, global-local higher-order theory GLHT-32 isproposed by considering transverse normal strain of 1,2-3 global-local higher-ordertheory. Numerical results show that GLHT-32 is suitable for predicting thermal responseof laminated plates under uniform temperature. ●This thesis further developes the global-local higher-order theory GLHT-52 which canaccuratelly predict thermal response of angle-ply laminated plates subjected to arbitrarytemperature loads. This work extends the range of applicability of the global-localhigher-order theory.●It is well known that the free-edge problem is a typical three-dimensional problem.Three-dimensional finite elements and layerwise theories have to be used to analyzefree-edge effects because previous equivalent single layer plate theories can not analyzeso complicated problem. By increasing the number of order of in-plane and transversedisplacements, an enhanced global-local higher-order theory GLHT-mn has beendeveloped to analyze free-edge problems. Numerical results show that GLHT-99 which isa typical equivalent single layer plate theory is able to predict accurately static responseof the free-edge effects. Thereby, this work directly proves that equivalent single layerplate theory can analyze free-edge problems of laminated plates.●Global-local higher-order laminated shell theory GLHST-52 as well as correspondinganalytical results have been given in this thesis. Unknown variables of this theory areindependent of number of layers and transverse shear stresses can be directly computedfrom constitutive equations. Numerical results show that present shell theory is moreaccurate than other shell models.2. Based on global-local higher-order theory, this thesis detailedly studies laminatedplate elements.●Based on the refined nonconforming element method, a refined four-node quadrilateralplate element RQLP13 and a refined three-node triangular element RTLP23 are presented.Subsequently, a triangular plate element TLP13 and a quadrilateral plate element QLP19are also proposed by using the discrete Kirchhoff thin plate bending element satisfying C¹continuity on the element boundary. Global-local higher-order theory possesses first andsecond derivatives of transverse displacement w in the strain components. Thustransverse displacement function satisfying C⁰ as well as C¹ continuity on the elementboundary, which is named as C^0-1 continuity, should be employed. This thesiscircumvents the requirement of C^0-1 continuity by using C⁰ continuity displacementfunction and C¹ continuity displacement function, respectively. Finite element modelsconstructed in this thesis are simple and are convenient to use, which are suitable for allkinds of cases without any numerical technique. Moreover, they exhibit goodperformance for both regular and irregular meshes.●Based on 1,2-3 global-local higher order theory, laminated plate elements for vibration and buckling analysis are given. Furthermore, the modified geometric stiffness matrixmethod is extended to buckling problems of laminated composite plate. By using ourapproaches, dynamic and buckling problems on soft-core sandwich plates as well aslaminated composite plates with different thickness and materials at each ply have beenanalyzed. Numerical results show that first order theories even global higher-ordertheories are inadequate to predict dynamic and buckling response of so special structureswhereas 1,2-3 global-local higher order theory is still suitable for analyzing dynamic andbuckling problems of laminated composite plates with variational thickness and materialsat each layer and soft-core sandwich plates.●Combining 1,2-3 global-local higher order theory and layerwise theory, the mixed modelis developed in this thesis. This model is used to analyze bending problems of laminatedpiezoelectric plates. Moreover, effects of electric displacement on static response oflaminated piezoelectric plates are also studied. The concept of mixed model is that themechanical component is modeled by 1,2-3 global-local higher-order theory whereas theelectric field is modeled with layerwise theory. Present mixed model is able to accuratelypredict transverse shear stresses of laminated piezoelectric plate without any smoothingmethods.●Geometrically nonlinear finite element based on 1,2-3 global-local higher-order theoryhas been constructed, which is used for geometrically nonlinear analysis of laminatedplates. Numerical results show that for geometrically nonlinear analysis, effect of thesecond-order components in in-plane displacement on transverse shear stresses is actuallysignificant.