A New Method For Analyzing The Equivalent Stiffness Of Orthotropic Plates

This thesis mainly studies the equivalent stiffness of orthotropic plates on the structure.The types of plates studied are divided into four main types: semi-circular arc corrugated plate,trapezoidal corrugated plate,hemispherical convex concave-convex plate and symmetrical trapezoidal convex plate.The above-mentioned plates are widely used in various constructions such as housing construction,ships,and bridges.First,the second principal stiffness formulas of semicircular arc-shaped corrugated plate and trapezoidal corrugated plate were derived by using the theory of linear elasticity in the bending process of thin plates and the equivalent deformation theory in material mechanics.Combined with ANSYS finite element analysis software to verify the difference between the numerical simulation solution and the deflection solution obtained by the Navier method,and discussed the influence of different representative voxel structures on the accuracy of the equivalent stiffness obtained and the solid construction template under different boundary conditions The results were compared with the finite element of an equivalent plate to verify the correctness of the equivalent stiffness.Next,the equivalent stiffness combination method and the principle of integral homogenization were used to study the equivalent stiffness of the hemispherical convex plate and the symmetrical trapezoid convex plate.The influence of the structural dimensions of representative voxels and the constraints of the plate boundary in engineering practice had fully verified the correctness and reliability of the equivalent stiffness formula solved in this paper from a static perspective.Finally,the vibration characteristics of orthotropic plates are studied,and semicircular convex plates and symmetrical trapezoid convex plates are selected as models.By comparing the first-fourth-order natural frequency finite-element numerical simulation solutions and theoretical solutions of a square macroscopic plate structure with four-sided simple support,it is verified that the equivalent stiffness is also applicable to vibration problems.Then the first three orders of natural frequencies and principal modes of the solid model and equivalent plate under the three boundary conditions of four-sided fixed,opposite fixed and simply supported are compared respectively,and the comparison results are basically consistent.This paper proposes a new method for analyzing the equivalent stiffness of an orthotropic plate.This method obtains the functional representation of the representative voxel cross section by establishing a plane rectangular coordinate system,and then the equivalent stiffness of the orthogonal anisotropic plate can be conveniently obtained through the solution formula proposed in this paper.Compared with the previous work,the calculation method in this paper is simple and fast.It does not need to calculate the equivalent stiffness by calculating the inertia moment of the complex section,and it also avoids the problems of large workload and inaccurate results caused by the equivalent stiffness obtained by numerical simulation.