Micromechanical Analysis Of Composite Materials Based On Improved Lobatto Element

Composite materials have been widely used in aerospace,automobile and other engineering applications because of their superior specific stiffness,high specific strength and designability.The analysis of mechanical response and strength failure of composite materials is the key to solving the application problems of composite materials.It is of great significance to the study of new methods and techniques for the analysis of mechanical behavior of composite materials.In recent decades,a large number of scholars have carried out a lot of research on this from experimental,theoretical and numerical aspects.Based on the properties of composites(fibers and matrix),the theory of composite mesomechanics predicts the equivalent properties of composites and analyses their failure characteristics.At present,there are many mature theoretical models of mesomechanics.Bridge model is one of them,which has the characteristics of simple form and high accuracy,and is convenient to combine with various numerical methods.Lobatto element is a kind of element form based on non-equidistant Lobatto nodes.Because the mass matrix obtained by Lobatto integral has diagonalization characteristics,it is especially suitable for dynamic analysis.In recent years,Lobatto element is widely used in such fields as acoustics,dynamics(impact),structural damage detection,structural health monitoring,seismology,etc.Medical imaging and computational fluid dynamics.At the same time,it has been successfully applied in the dynamic analysis of composite materials.This paper focuses on the improvement and applicability of Lobatto element and the bridging theory of composite micro-mechanics.Through numerical algorithm research,the basic algorithm of Lobatto element and the applicability of its improved form are studied.On the other hand,the application of Lobatto element and bridging theory is studied in the field of composite materials.The main research contents are as follows:(1)Aiming at the Lobatto element modified by assumed natural strain method(ANS),its applicability in anisotropic material plates is discussed.The theoretical analytical solutions of typical thin plates are obtained,and the computational results of ANS modified Lobatto element and traditional Lobatto element are compared.The numerical results show that the accuracy of the ANS-improved Lobatto element is significantly higher than that of the traditional Lobatto element under the same grid density,which verifies the applicability of the ANS-improved Lobatto element in the analysis of anisotropic material plates.(2)The improved Lobatto element of ANS is combined with the bridge model to apply in the field of mechanical analysis of composite materials.The bridge model provides the material parameters of single-layer and laminated plates for macro-analysis using ANS-improved Lobtatto element.The analysis based on ANS-improved Lobtatto element provides more accurate displacement and plate rotation results for the bridge model.Further,the stress in the fiber and matrix components can be obtained.In this paper,the feasibility of this cross-scale analysis method is verified by numerical examples.(3)The ANS modified Lobatto element is extended to the dynamic analysis.The dynamic response of plates with different thickness is studied by applying the ANS modified Lobatto element.The dynamic stress changes in the fiber and matrix components are calculated by combining the ANS modified Lobatto element with the bridge model.