اجزا محدود غیر خطی

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شرح پروژه

اجزا محدود غیرخطی

Nonlinear Finite Element Methods

Assignment for winter term 2018/19

A simple horizontal rod of length l = 10mm is clamped at the left end while at the right end

a displacement u is applied. The cross section area A of the rod is given as A = 1mm2. The

displacement u is applied gradually as a function of time starting from u = 0mm at time

= 0s up to a final value uend = 1:0mm at = 1s.

Task description

Create a Finite-Element program to solve the problem described above for an arbitrary number

of finite elements and time increments, respectively. The nonlinear nature of the problem due

to nonlinear material behaviour has to be taken into account. Use Matlab or Python and please

note that the program should consist of at least three modules: main program, element routine

and material routine.

Finite Elements with linear approximations for the displacement should be employed. Use the

constitutive law (material) and the integration method according to your particular variant. Each

student has to work on that variant that corresponds to the last digit of his or her matriculation

number. The integration of the constitutive law by means of the Euler explicit scheme has to be

implemented as well.

variant constitutive law parameters integration scheme

1 _ = E"_ ? E

E = 1GPa; = 104 Ns

mm2 Euler implicit

2 _ = E"_ ? E

Runge-Kutta 2nd order explicit

3 _ = E"_ ? E

Runge-Kutta 2nd order implicit

4 _ = kb(1 ?

k )"_ k = 1MPa; b = 75 Euler implicit

5 _ = kb(1 ?

k )"_ Runge-Kutta 2nd order explicit

6 _ = kb(1 ?

k )"_ Runge-Kutta 2nd order implicit

7 _ = 0

"0

"_

1+(=0)n?1n 0 = 1Pa; "0 = 0:01; n = 2 Euler implicit

8 _ = 0

"0

"_

1+(=0)n?1n Runge-Kutta 2nd order explicit

9 _ = 0

"0

"_

1+(=0)n?1n Runge-Kutta 2nd order implicit

Note:

The successful completition of the task is a prerequisite to be admitted to the final examination.

The deadline for the assignment is Friday, 8th of february, 2019 when the program has to be

sent to Geralf.Huetter@imfd.tu-freiberg.de and the documentation has to be in hard-copy form

at secretary of the institute (room WEI-130). Each student has to present his or her program

individually to the lecturer in the subsequent week.

این پروژه شامل 1 فایل مهم است، لطفا قبل از ارسال پیشنهاد حتما نسبت به بررسی این فایل اقدام فرمایید.

مهارت ها و تخصص های مورد نیاز

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