Inverse Finite Element Method For Dynamic And Static Displacement Field Reconstruction Of Plate And Shell Structures

As the development of science and technology and the improvement of people's living standards,people's requirement for environmental safety are getting higher and higher.In order to improve the safety of the environment,it is necessary to carry out structural health monitoring on large structures and machinery.Structural health monitoring uses sensor network systems to provide real-time information about the overall or local structural state of the structure.The inverse finite element method is a novel method of full-field displacement reconstruction using strain data measured by a strain sensor network system.The inverse finite element method is based only on the strain-displacement relationship and does not require a force balance equation.Therefore,the static and dynamic displacement fields can be reconstructed without the knowledgement of material properties,loading loads,and damping characteristics.In this paper,a new eight-node hexahedron solid-shell element is presented.According to the basic theory of finite element method,the formulation of the element is derived by applying the isoparametric transformation.The shear and trapezoidal locking and thickness and membrain locking in the element are briefly introduced.The assumed natural strain and the enhanced assumed strain are presented for solving the locking phenomenons effectively.The stability and accuracy of the eight-node hexahedral solid-shell element in simulating different morphological structures are verified by examples.Based on the inverse finite element theory,the error between the calculated strain and the measured strain is minimized by the least squares variation method.The inverse finite element formula of the eight-node inverse hexahedral solid shell element is derived.The accuracy and efficiency of the inverse finite element model is verified by the displacement field reconstruction of a cantilever plate and a thin-walled cylinder.Taking the forced vibration of the cantilever beam as an example,the inverse finite element method is used to reconstruct the dynamic response of the cantilever beam under different load frequencies.It is proved that the real-time reconstruction of the dynamic displacement field can be realized by the surface strain data of the structure.