• Journal of Advanced Marine Engineering and Technology
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• v.14 no.4
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• pp.46-56
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• 1990

Stress analysis of axi-symetric body with non-symetric loading and non-symetric given displacements is investigated in this paper using the finite element method. As the non-symetric load and non-symetric given displacements of axi-symetric body are generally periodic functions of angle .theta., the nodal forces and nodal displacements can be expanded in cosine and sine series, that is, Fourier series. Furthermore, using Euler's formula, the cosine and sine series can be converted into exponential series and it is prooved that the related calculus become more clear. Substituting the nodal displacements expanded in Fourier series into the strain components of cylindrical coordinates system, the element strains are expressed in series form and by the principal of virtual work, the element stiffness martix and element load vector are obtained for each order. It is also showed that if the non-symetric loads are even or odd functions of angle ${\theta}$ the stiffness matrix and load vector of the system are composed with only real numbers and relatively small capacity fo computer memory is enough for calculation.

• Journal of Advanced Marine Engineering and Technology
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• v.18 no.3
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• pp.1-9
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• 1994

The transient temperature distribution of materials during upsetting forming is very important for quality of upsetted workpiece and understanding the thermal characteristics of upsetting is essential for optimum control of the forming. In this paper it is shown that the governing equation of heat transfer for axi-symetric body can be derived from minimizing a functional, and from this theory, formulation of analysis by the finite element method is presented. It is also shown that the thermal contact resistance between two bodies can be represented by equivalent coefficient of heat conductivity. Some examples of calsulated transient temperature distributions by the computer program diveloped from the theory presented in this paper are given in graphic forms. It is proven that the results calculations are very plausible.