A Study On The Equivalent Bending Stiffness And Mechanical Properties Of The Periodic Raised Plate Structure

The periodic raised plate structure is a new type of lightweight.It is by stamping and rolling typical unit with periodic homogenization characteristics on foundation plate.Because of these complex microstructures,the periodic raised plate has the mechanical properties of structure orthogonal anisotropic and higher bending stiffness,strength and reliability than foundation plate.Compared with the sandwich plate and laminated plate,the periodic raised plate structure has excellent mechanical properties such as plane compression and shear ability,high temperature stability and fatigue resistance,high designable and energy absorption capacity.It also has the advantages of simple fabrication techniques and lower cost.Because the periodic raised plate structure is a new research direction in recent years,most of the research results of it are confined to the fabrication technology,the static and dynamic properties of it are seldom studied.The structure orthogonal anisotropic corrugated plate and square corrugated plate belongs to the basic structure of the periodic raised plate structure.In this paper,the static and dynamic characteristics of corrugated plate,square corrugated plate and the periodic raised plate structure with various raised shapes are studied.Based on Kirchhoff's theory of small deflection bending of orthotropic plates,the solution of the bending problem of orthotropic plates with four simply supported edges under concentrated loads is obtained by using Navier method.The vibration function is taken as a trigonometric series,the natural frequency and vibration mode of free vibration of structure orthogonal anisotropic plate are given.The corrugated plate stiffness formula of Seydel is discussed,and the limitation of its second main stiffness formula is pointed out by finite element method.Based on classical theory of elastic thin plate and moment of inertia of corrugated section,the equivalent stiffness formulas of corrugated plate and square corrugated plate are given,and the finite element method is used to validate it from both static and dynamic aspects.The natural vibration characteristic of corrugated plate is studied,and the influence of geometric structure parameters on it is analyzed.According to the periodic homogeneous distribution characteristics of typical units of periodic raised plate structure,based on the small deformation of elastic thin plate and linear elastic deformation theory,four basic assumptions of macro structure of periodic raised plate are given.Based on the classical theory of elastic thin plate,moment of inertia,calculus,and the stiffness combination equivalent method proposed in this paper,a new analytical method for calculating the equivalent stiffness of periodic raised plate structure is presented.Four kinds of periodic raised plate structure,trapezoidal,triangular,arc and sine wave periodic raised structure plate are studied by using the method presented in this paper,and the equivalent stiffness formulas are given.Based on the finite element method,Navier method and equivalent plate comparison method with different boundary conditions are applied to verify the correctness and accuracy of the analytical method in this paper.The influence of geometric structure parameters of typical units of periodic raised plate with each type of raised structure on the equivalent stiffness characteristics of this paper is studied,and the reasons are analyzed.According to the natural vibration characteristics of periodic raised plate structure,the first four orders frequency are calculated by using the equivalent stiffness given in this paper.By comparing the results of finite element modal analysis,the equivalent stiffness given in this paper is verified in terms of dynamics.Taking the sine wave periodic raised structure plate as an example,the influence of geometric structure parameters of typical unit on its natural vibration characteristics is given,and the reasons are analyzed.Based on the equivalent stiffness analytical method and periodic homogenization characteristics of periodic raised plate structure,the optimized design scheme for equivalent performance is proposed through the design of typical unit geometric structure parameters.The triangular periodic raised structure plate is selected as an example to optimize the design,and the optimization results are discussed and analyzed.The results of the study have important meanings for the statics and dynamics researches of the periodic raised plate structure and practical engineering application.