nonlinear theory of elasticity question using Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg48122] nonlinear theory of elasticity question using Mathematica*From*: Anatoly Vershinin <versh1984 at mail.ru>*Date*: Fri, 14 May 2004 00:12:21 -0400 (EDT)*References*: <c7q6c7$rph$1@smc.vnet.net> <200405130408.AAA26744@smc.vnet.net>*Reply-to*: Anatoly Vershinin <versh1984 at mail.ru>*Sender*: owner-wri-mathgroup at wolfram.com

Thursday, May 13, 2004, 8:08:52 AM, Narasimham G.L wrote: NGL> Did you first solve the linear case with circular hole? Is the time NGL> taken more due to inclusion of geometrical non-linearity? Is the NGL> material isotropic or St.Venant type? Please send details of the NGL> Stress function, whether plane stress/strain , PDEs, compatibility NGL> conditions,boundary conditions etc. Using NDSolve should take only a NGL> few seconds.I have not used the tensor package of Mathematica but NGL> believe it should be not too difficult or time consuming. First of all thanks for your answer. My programs consist of two principal steps: at first it solve the linear case, then using it program calculates nonlinear approximation of the task. You were right about geometrical nonlinearity. If I set semi-axes of ellipse equal, then the duration of calculation will be about 3-5 minutes, depending on number of elements of row. All stresses and strains are plane. The nonlinear properties of given material are described by Murnaghan potential. I don't use NDSolve because there are no numerical calculus in program. All steps(including the answer) are symbolical. Boundary conditions consist in null stress on the boundary of elliptical hole. For solving I use Kolosov-Mushelishvili complex potentials, expanding them to finite row. Because of large symbolical expressions tensor operations, integration and especially Symplify and FullSimplify, which use these expressions are very time consuming. By the way, where can I get tensor package of Mathematica, as in the program I had to wrote some tensor functions myself (I didn't find in Mathematica nabla operator, convolution product and other operations, which can be applied to tensors). -- Best regards, Anatoly mailto:versh1984 at mail.ru

**References**:**Re: nonlinear theory of elasticity question using Mathematica***From:*mathma18@hotmail.com (Narasimham G.L.)