The Scientific Bulletin of VALAHIA University MATERIALS and MECHANICS –Vol. 16, No. 14 DOI 10.1515/bsmm-2018-0010 DISPLACEMENT STATES FOR ISOTROPIC PLATES Carmen POPA 1 , Violeta ANGHELINA 1 , Octavian MUNTEANU 2 1 Valahia University Targoviste, Romania, 2 KPD Construction Software, Halen, Belgium E-mail: carmenpopa2001@yahoo.com Abstract. In this paper the deformation state of a circular and isotropic plate is analyzed, using as methods of comparison the analytical, the finite element and the experimental element methods. In the finite element method, the plate is analyzed by several programmes, as well as assembled with the respective container. Keywords: Plate, Analitical method, Finite element method, Experimental method 1. INTRODUCTION The circular plates are met in diverse engineering constructions. They are used like circular plates for the foundations of some machines, at the coupling of the pipes and others. The researches for establish the states of deformations and stresses can be grouped in: mathematical methods of calculation [1-3]; numerical methods [4-6]; experimental methods [7 -11]. 2. ANALITICAL METHOD We consider a recipient with a fixed circular plate. The plate has the following dimensions: diameter  = 650 mm and thickness h = 10 mm, like in Figure 1. Figure 1. The geometrical characteristics of the plate The ensemble is loaded with a uniform distributed charge p = 0,2 MPa. Because the load is axial- symmetrically, the median plane of the plate will be deformed axial- symmetrically, too. The bending parameters of plate depend of its thickness, as against the others dimensions of the plate. If the displacement “ w ” of a plate is short, as against its thickness, we can allow these hypotheses: - the median surface of the plate doesn’t permit extensions. This plane remains a neutral plane in the due time of the bending of the plane; - the points of the plate, which are on a normal straight line, remain on a normal straight line at the median surface of the deformed plate; - the normal stresses after the normal direction of the median surface of the plate can be neglected; From the differential equation for the axial-symmetrical bending of the circular plates, which are solicited transversal [1], it results: D T dr dw r 1 dr w d r 1 dr w d 2 2 2 3 3    (1) We obtain the displacements: 3 2 2 1 4 C r ln C 4 r C D 64 r p w        (2) In these relations: w represents the deflection; T – the shearing force;  - the slope angle; r - the current radius; 3 2 1 C , C , C - the integrating constants; D – the bending rigidity of the plate, which has the expression:   2 3 1 12 h E D      , (3) where: E is the modulus of longitudinal elasticity of the plate material;  - the coefficient of the transversal contraction (the Young s coefficient). 32 gauri Ø23 10 32 holes  23 64