Research On The Dynamic Characteristics For The Curvilinearly Stiffened Kirchhoff-Mindlin Plate

Stiffened plates are a kind of combination structures developed by adding stiffeners to the plates in different types of lay-ups.Stiffeners make it possible for the stiffened plate to sustain highly directional loads.Compared with a traditional plate,stiffeners could not only increase bending stiffness of the stiffened plate with a minimum of additional material,but also introduce multiple load paths which provide protection against damage and crack growth under the compressive and tensile loads.Hence,stiffened plates are known as one of the major forms of pressure-resistant structures.They have been widely used in kinds of industries such as aerospace,transportation,marine ships and constructions due to their excellent performance in easy-fabricating,specific strength,lightweight and loads capacity,etc.Compared with straight-line stiffeners,curve stiffeners perform much better in improving the mechanical properties of the plate.For finite element analysis(FEA)of stiffened plates,two methods are widely used.One is the Kirchhoff theory(i.e.,the classic plate theory)which is suitable for thin plates,and the other is the Reissner-Mindlin theory which is suitable for thick plates.Although the transverse shear deformation is considered in the Reissner-Mindlin theory,shear locking and zero energy mode are easy to occur for a thin plate.So it is urgent to develop a new FEA method which could be suitable for both thin and thick plates.The main works carried out in this paper are as follows,Finite element(FE)theory for dynamic analysis of curve stiffened plates is derived.A new FE method which is suitable for dynamic analysis of both thin and thick plates is developed.In the discrete Kirchhoff-Mindlin theory,shear locking and zero energy mode problems are evitable by assuming the discrete constrains of the shear strain field and the boundary of elements.For the free vibration analysis of curve stiffened Kirchhoff-Mindlin plates,discrete Kirchhoff-Mindlin triangular elements(DKMT)and Timoshenko curve beam elements are used to simulate the plate and stiffeners,respectively.FE formulations based on the displacements of plate elements are established by using the displacement interpolation functions of plate and the displacement coordination conditions of the stiffener interface.The dynamic characteristic analysis of a curved stiffened plate and the normal temperature modal test are studied by using the finite element theory of the dynamic characteristic analysis of a curved stiffened plate.In order to verify the validity and accuracy of the method,the dynamic characteristics of the straight stiffened plate with double straight tendons are analyzed.The results of the natural frequency calculation are compared with the experimental and simulation results in the literature.Secondly,the single bar curve stiffened plate is analyzed,and its natural frequency and vibration mode results are obtained,and the results are compared with the results of the literature and finite element software simulation.At last,the normal temperature modal test of single bar curve stiffened plate is carried out,and the results are compared with the experimental results by the analysis of the natural frequency and vibration mode obtained in this paper.Through the above analysis,the accuracy of this method is verified.The effect of size parameters on the dynamic characteristics of a curved stiffened plate is studied.Based on the theory of Kirchhoff-Mindlin plate,the model of square plate,circular plate and elliptical plate in the center is established.The finite element model of the curve stiffener is established by the theory of Timoshenko beam.The plate element grid is divided by Distmesh.The geometric and finite element models of the curve bar are obtained through the 3 order B spline curve.The finite element models of the stiffened square plate,the circular plate and the elliptical plate are established respectively.First,the exact finite element model is obtained by verifying the convergence and veracity.Secondly,the influence of the size parameters on the natural frequency of the square plate,the circular plate and the elliptical plate of the central band hole curve is carried out.The influence of bar layout,rib curvature,reinforcement thickness and thickness parameters on the overall natural frequency of the structure is also studied.