Research On Displacement Models Of Laminated/Sandwich Structures And Numerical Methods Of Viscoelastic Structures Based On Layerwise Theory

Due to the features of high strength-to-weight ratio,high stiffness-to-weight ratio,fatigue-resistence,and designability,laminated composite and sandwich structures have been widely used in aeronaustic and aerospace,ocean,high speed trains,automobile and many other engineering fields,However,due to the heterogeneity and anisotropy along the thickness direction,the mechanical properties of the laminated composite and sandwich structures are more complicated compared with conventional single layer structures,and the interlaminar shear stiffness of the adhensive joints in laminated composite and sandwich structures is weak,which is prone to interlaminar damage and delamination failure.Interlaminar transverse shear stress is one of the key factors for initial delamination failure of composite structures,and therefore,accurate modeling of laminated composite and sandwich structures is of great significance to provide accurate predictions for the through the thickness distributions of the stress fields,especially the transverse shear stress field.The structure sandwiched with viscoelastic damping material is one of typical sandwich composite structures.With the introduction of the viscoelastic damping material,viscoelastic sandwich structures also have good vibration and noise suppression effects in addition to the performance advantages of high strength-to-weight ratio and stiffness-to-weight ratio,and therefore,the application of the viscoelastic sandwich structures in engineering are more and more popular in recent years.However,as the constitutive relation of the viscoelastic material is time,frequency and temperature dependent,choosing the appropriate viscoelastic constitutive model and how to accurately formulate the element of the viscoelastic sandwich composite structure for numerical predictions of vibration and damping characteristics have always beem hot and difficult problems in engineering analysis.In this thesis,two aspects of research work on the above mentioned key problems of laminated composite and structure studies are conducted.On the one hand,the studies forcus on how to develop a high accuracy displacement field model for laminated composite and sandwich structures.With the framework of higher order Layerwise theories,a displacement description model considering the interlaminar transverse shear stress continuity of laminated composite and sandwich structures is proposed,and a simplified but effective five-variable displacement field model is further presented for three-layer sandwich structures.On the other hand,numerical studies on dynamic analysis of viscoelastic sandwich structures are presented,including the proposal of a generalized viscoelastic constitutive model and the formulations of an arbitrary quadrilateral element and a high accuray rectangular element for viscoelastic sandwich structures.The specific research contents of this thesis include:(1)A displacement description model considering the interlaminar continuity of transverse shear stress and its numerical validation.At present:most of Layerwise theoretical models for laminated composite and sandwich structures arc formulated based on the layerwise description of displacement fields.Most of these theoretical models violate the interlaminar continuity of transverse shear stress.Within the fralework of higher order Layerwise theories,this thesis presented a displacement field model of laminated composite and sandwich beams based on layerwise description of transverse shear stress field.First,the quadratic distribution of transverse shear stress field along the thickness direction of each layer of the laminated composite and sandwich beam is considered,and the distribution function of the transverse shear stress field in each layer is formulated by the superposition of linear and parabolic functions.The interlaminar continuity of transverse shear stress field is a priori fulfilled with the introduction of transverse shear stress variables defined on surfaces of each discrete layer.Then,the transverse shear strain and inplane displacement of each layer are deduced based on the constitutive relations and geometric equations.With further consideration of interlaminar continuity of inplane displacement and boundary conditions at the top and bottom surfaces,the transverse shear stress variables defined on surfaces of each discrete layers are elaminated,and then,the final expression the higher order layerwise displacement expression of the laminated composite and sandwich beam which has only displacement variables are obtained.Numerical examples fully validate the proposed displacement model can accurately predict the distributions of stress and displacement fields along the thickness direction of laminated composite and sandwich structures.(2)Construction of a five-variable displacement model for a three-layer sandwich beam with soft core.For sandwich structures with soft core,the stiffness difference between the core layer and the face layers is significant,and the variation of the transverse shear stress field is not various.Therefore,unlike the quadratic distribution assumption of transverse shear stress in each discrete layer,this section consider the transverse shear stress field follows constant distribution along the thickness of the soft core layer and quadratic distribution in the moderately thick face layers with the consideration of the interlaminar continuity.In this formulation,the variables describing the transverse shear stress field of the three-layer sandwich beam are simplified from five in the above section to three,and the final displacement field expression has only five variables.Compared with seven variables in the above section,the complexity of displacement field description is greatly reduced.Moreover,comparsions with the displacement expressions of some classical models refect that these classical models are actually degenerate forms of the present five-variable displacement model,but these classical displacement models don’t have the ability to describe the interlaminar continuity of transverse shear stress and warping deformation of the cross section of moderately face layers.Numerical validation and discussion fully reflect the high accuracy of the presented five-variable displacement Held model for static and dynamic analysis of both thin and thick sandwich beams with soft core.(3)For dynamic analysis of viscoelastic composite structures.a generalized Burgers viscoelastic constitutive model is proposed,and a comprehensive approach of the application of the generalized model in dynamic analysis of viscoelastic composite structures is presented.Based on the classical Burgers model,this thesis extends the single Burgers model to multiple Burgers models connected in parallel,and introduces a spring model with parallel conection to describe the solid property of the viscoelastic material,and the number and parameters of the Burgers model can be optimized and adjusted as required.Therefore,a generalized Burgers viscoelastic model which is scalable and accuracy controllable is formulated.Through the introduction of dissipate coordinates,the generalized model is applied to the finite element dynamic governing equations of viscoelastic composite structures with frequency dependent damping characteristics.Then,a complicated Volterra integro-differential equation is transformed into a standard second-order differential equation,and therefore,dynamical solution techniques for linear elastic structures can be used directly.Compared with the widely used GHM model,each mini-oscillator term of the generalized Burgers model has four parameters,while the GHM model has only three.Therefore,the proposed generalized model has higher accuracy in describing dynamic behaviors of viscoelastic structures,and the increase of parameters in each mini-oscillator term doesn’t increase the scale of the final equations.Numerical examples refect the high fitting accuracy for complex modulus of viscoelastic materials and the effectiveness of the dynamic analysis method for viscoelastic composite structures based on the generalized Burgers model.(4)An arbitrary quadrilateral element is formulated for dynamic analysis of constrained layer damping plate structures.At present,the finite element analysis of constrained layer damping plates basically adopts rectangular or triangular elements,but it will have difficulty in shape fitting or lack of precision when used to simulate irregular structural forms.This thesis presents a four-node arbitrary quadrilateral element for constrained layer damping plate based on Layerwise theory and discrete Kirchhoff assumption.The constrained layer and base layer of the contrained layer damping plate satisfy Kirchhoff plate theory,while the viscoelastic damping layer meets first order shear deformation theory.For the rotation variables of the constrained layer damping plate element,the formulation method of the discrete Kirchhoff quadrilateral plate element(DKQ)is employed.In this formulation,the displacement constraints of the Kirchhoff assumption at any point in the element are relaxed,and only enforced at corner nodes and mid-nodes at element sides.Moreover,the adjacent displacement of each element is ensured.Based on the finite element model,the vibration and damping characteristics of the constrained layer damping plate are studied.Numerical examples validate the analysis accuracy and the adaptability of the proposed quadrilateral element model to irregular structural forms and complex boundary conditions.(5)A high-precision elelent for dynalic analysis of sandwich plates with moderately thick viscoelastic core is presented.Most of previous studies neglected the transverse compressive effects of the viscoelastic layer.and the accuracy of engineering requirements is often not satisfied when analyzing sandwich structures with thick viscoelastic core or high frequency vibration problems.Based on higher order Layer·ise theoryr a high precision rectangular element for sandwich plates with moderately thick viscoelastic core is developed.The top and bottom layers satisfy Kirchhoff plate theory.while the moderately thick viscoelastic core meets higher-order deformation theory.According to the characteristics of moderately thick viscoelastic core,interpolation points along the thickness direction of the core layer are introduced to discrete the in-plane and transverse displacement field of the viscoelastic core.In this formulation,not only extension and shear deformation of the viscoelastic core are considered,but also the transverse shear deformation is effectively taken into account.On the basis of the displacement field expression,a high precision rectangular element formulation is developed.Numerical examples validate high accuracy of the present rectangular element,and it is found that:for the sandwich plate with thin viscoelastic core,the element model considering linear variation of the displacement field along the thickness direction can provide accurate predictions,but for sandwich plates with moderately thick viscoelastic core,the present element model considering higher-order variations in displacement fields have higher analysis accuracy.Moreover,it is also found by numerical discussion that when the modal loss facors are maximized,there exist optimal stiffness ratios between the surface layer and the viscoelastic core layer,and it has important reference value for the damping design in engineering structures.