Principles Of Complementary Energy With Mixed Variables For Bending Rectangular Plate And The Application

With the rapidly developing of national economy in recent years, highway communications, large industrial workshop and high-rise have developed quickly; elastic plates are widely used in engineering, especially rectangular plates are widely used in underground architectural engineering and water project. like underground diaphragm wall, sluice gate, runway of airfield and so on, are all construed as rectangular plate. It is difficult to get an uncomplicated solution to solve rectangular plate under complicated boundery condation. In some engineering practice, experience formulas and graphs were adopted, thus there were always big errors. Establishing a precise and reliable theory to practical process is becoming urgent. Thus this research is a matter of significance in theorem research and in engineering application.With the definitions of weakly admissible stress, weakly admissible displacement of equilibrium and the reciprocal theorem, this paper established the first and second principle of complementary energy with mixed variables in small deformation, two theorems of complementary energy with mixed variables are given out. The theorem of complementary energy with mixed variables of rectangular plate and the complementary energy equations of rectangular plate under different boundery conditions are given out. Compared with traditional methods of rectangular plate, P is introduced in expression of the second principle of complementary energy with mixed variables, the method to solve the equations of the deflection surface is been simplified. The bending rectangular plate with different boundary conditions under different loads, such as with four edges simply supported under concentrated load or uniform load; four edges fixed under uniform load; four corner points supported under uniform load; two adjacent edges free and the other two adjacent edges fixed under uniform load etc. are solved with the second complementary energy theorem. The equations of the deflection surface and the numerical values were given out. Compared with the results of ANSYS and the experimental results, the method of this paper is correct and general in solving the rectangular plate problems. Finally, the method introduced in this paper can be applied to solve the actual project, giving the actual project more since numerical values.