Study on Combined shell Mechanics Analysis

Xiangzhong Meng College of Marine, Northwestern Polytechnical University, Xi’an 710072, China Tel: 86-29-8847-4122 E-mail: mengxz@mail.nwpu.edu.cn Xiuhua Shi & Xiangdang Du College of Marine, Northwestern Polytechnical University, Xi’an, 710072, China The research is supported by graduate starting seed foundation of Northwestern Polytechnical University. No. Z200510. Abstract The AUV combines mostly in ball shell, cylindrical shell, taper shells and other rotary shells by thread coupling, bolt coupling, wedge coupling and hoop coupling. This paper makes the finite element analysis and research on the mechanics mode of a certain AUV with the analytic method. Based on the basic equation of theory of thin shells, analysed every separated shells, and set up it’s mechanics mathematical model, and analysed the combined shell with the finite element method. At last, the final result validated the mathematical model. The method presented is effective in analysing and dynamical designing of AUV structure.


The basic theoretical equation of thin shell
A middle surface patch of thin shell and internal forces on the cross section are shown in figure 2. The parameters 1 N , 2 N , 12 N , 1 M , 2 M , 12 M , 1 Q , 2 Q are the internal forces acted on α plane and β plane, 1 k and 2 k are the main curvatures on α direction and β direction, 1 R and 2 R are the radius of main curvature on the middle surface, and , A and B are the Lame coefficients on α direction and β direction, 1 p , 2 p , 3 p are the component of loads on α direction , β direction and γ direction, u , v and w are the component of displacements on α direction, β direction and γ direction of any point on the middle surface of shell.
The balanceable equations of basic equation in the thin shell theory are: From the geometrical equations (1.2) and the physical equations (1.3) of basic equation in the thin shell theory, we can reason out the elastic equations (1.4). 1) The state of nonmomental theory supposed there are no both flexural moment and torsional moment on the any cross section of the thin shell, that is

The Cylindrical Shell
The α -axis point to the generatrix and the β -axis point to the circumference of cylindrical shell, then, 1 0 k = , 2 1 k R = and 1 A B = = , the Gauss-Codazzi conditions are fulfiled.It is shown in figure 3. The balanceable equations and elastic equations of cylindrical shell nonmomental theory are:

The Gyral Shell
The parameter 1 C is the curvature center of point M on the gyral shell generatrix.It is shown in figure 4. The curvatures are 1 The balanceable equations and elastic equations of gyral shell nonmomental theory are: The ball shell is the special gyral shell, and in the ball shell.

The Axial Symmetrical Bending Equations Of Cylindrical Shell
The internal forces, displacements and strains are axial symmetrical in the cylindrical shell.The internal forces reduce to 1 N , 2 N , 1 M , 2 M , 1 Q , and the displacements reduce to u , w .The axial symmetrical bending equations of the cylindrical shell are: ( 2 . 2 ) The approximate solution of equations (2.2) is made up of the nonmomental theory solution ( * w ) and the edge effect solution ( 0 w ), that is, In the equation (2.3), the edge effect solution ( 0 w ) is the solution on the effect of the flexural moment ( 0 M ) and the lateral shearing force ( 0 Q ) that are equally distributed along the boundary at the side of Where, 1 .

The Axial Symmetrical Bending Equations Of Gyral Shell
The parameters of the gyral shell, 1 , and on the condition of axial symmetrical bend, 12 and 2 0 p = , the axial symmetrical bending balanceable equations of the gyral shell are: The approximate solution of equations (2.5) is made up of the general solution of the homogeneous equation and the special solution of the unhomogeneous equation.The special solution can be solved from the nonmomental theory equations, and the general solution , the edge effect solution, can be solved by hybrid method.Then the equations (2.5) simplified to the equations (2.6).
The basic functions are supposed, .
The basic differential equations that the axial symmetrical bending edge effect of gyral shell are: To ball shell, the curvature radius are constants, and The effect of edge effect reduce rapidly with the distance increase to boundary, then the equations (2.8) simplified to the equations (2.9): The basic differential equations that the axial symmetrical bending of ball shell are: , where The internal forces expressions are:

The analysisi of torpedo
The shell of torpedo is made up of ball shell, cylindrical shell, taper shells and other rotary shells by thread coupling, bolt coupling, wedge coupling and hoop coupling.All of them are rigid coupling.The radius of ball shell Obviously, the circumferential direction internal force is not continuous on the coupling circumference, that , so, there is a direct displacement, and the radial alterations are: , and the cylindrical shell is The difference is ,where .
The parameters are counted, then, The results of the cylindrical shell are: The results of the ball shell are: As a result, the circumferential direction internal force is not continuous on the coupling circumference.Mechanical Systems and Signal Processing. 18. 367-380. Xu, zhilun. (1982).Elastomechanics.The High Education Press.

References
the force analysis of the coupling of the ball shell and the cylindrical shell in figure5.From the balanceable equations of ball shell nonmomental theory, and

0 M
the circumference, so that the continuousness of the internal force and displacement are ensured.Based on the theory of Timashenko, the rotations of the ball shell and the cylindrical shell are same along the circumference, so 0 = , and the discontinuousness is avoided enough by 0 Q .The direct displacement of the ball shell brought by 0