Análises não lineares no ANSYS

Exemplo 01: Não linearidade geométrica de viga engastada

Para resolver esse problema a carga será adicionada incrementalmente. Depois de cada incremento a matriz de rigidez será ajustada antes do novo aumento da carga.

Dados: Elemento BEAM 3Área da seção: 0.03125Izz: 4.069e-5Altura da viga: 0.124E: 30e06Poisson: 0.3Comprimento de cada elemento: 0.1 – 50 elementos e 51 nós

Solução:

Solution>New Analysis>StaticSolution>Analysis Type>Sol’n Control

A – Garante que sejam permitidos grandes deslocamentos

B- Ensure Automatic time stepping is on. Automatic time stepping allows ANSYS to determine appropriate sizes to break the load steps into. Decreasing the step size usually ensures better accuracy, however, this takes time. The Automatic Time Step feature will determine an appropriate balance. This feature also activates the ANSYS bisection feature which will allow recovery if convergence fails.

C – Números de substeps. Configura para que o substep incial seja de 1/5 da carga total.

Assume that the applied load is 100 lb*in. If the Automatic Time Stepping was off, there would be 5 load steps (each increasing by 1/5 th of the total load):

20 lb*in 40 lb*in 60 lb*in 80 lb*in 100 lb*in

Now, with the Automatic Time Stepping is on, the first step size will still be 20 lb*in. However, the remaining substeps will be determined based on the response of the material due to the previous load increment.

D – Para o programa se a solução não convergir até o número máximo de 1000 steps.

E – número mínimo de substeps de 1

F- garante que todos os tipos de solução serão escritos no arquivo de resultados.

Numa análise linear, para pequenos deslocamentos, não haveria deflexão nodal na direção x. Entretanto, para grandes deformações isto não é verdade.

PRINT U NODAL SOLUTION PER NODE ***** POST1 NODAL DEGREE OF FREEDOM LISTING ***** LOAD STEP= 0 SUBSTEP= 1 TIME= 1.0000 LOAD CASE= 0 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM NODE UY 1 0.0000 2 -1.0098 3 -0.40960E-03 4 -0.16384E-02 5 -0.36862E-02 6 -0.65530E-02 7 -0.10239E-01 8 -0.14743E-01 9 -0.20065E-01 10 -0.26205E-01 11 -0.33163E-01 12 -0.40937E-01 13 -0.49528E-01 14 -0.58935E-01 15 -0.69157E-01 16 -0.80194E-01 17 -0.92045E-01

18 -0.10471 19 -0.11818 20 -0.13247 21 -0.14757 22 -0.16347 23 -0.18019 24 -0.19771 25 -0.21604 26 -0.23517 27 -0.25511 28 -0.27585 29 -0.29738 30 -0.31972 31 -0.34286 32 -0.36679 33 -0.39152 34 -0.41704 35 -0.44335 36 -0.47045 37 -0.49833 ***** POST1 NODAL DEGREE OF FREEDOM LISTING ***** LOAD STEP= 0 SUBSTEP= 1 TIME= 1.0000 LOAD CASE= 0 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM NODE UY 38 -0.52701 39 -0.55647 40 -0.58670 41 -0.61772 42 -0.64952 43 -0.68209 44 -0.71544 45 -0.74956 46 -0.78444 47 -0.82009 48 -0.85651 49 -0.89369 50 -0.93163 51 -0.97032

MAXIMUM ABSOLUTE VALUES NODE 2 VALUE -1.0098

PRINT U NODAL SOLUTION PER NODE ***** POST1 NODAL DEGREE OF FREEDOM LISTING ***** LOAD STEP= 0 SUBSTEP= 1 TIME= 1.0000 LOAD CASE= 0 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM NODE UX 1 0.0000 2 -0.13863 3 -0.83886E-06 4 -0.83886E-05 5 -0.29359E-04 6 -0.70461E-04 7 -0.13840E-03

8 -0.23989E-03 9 -0.38162E-03 10 -0.57031E-03 11 -0.81264E-03 12 -0.11153E-02 13 -0.14850E-02 14 -0.19285E-02 15 -0.24523E-02 16 -0.30632E-02 17 -0.37679E-02 18 -0.45729E-02 19 -0.54851E-02 20 -0.65109E-02 21 -0.76571E-02 22 -0.89303E-02 23 -0.10337E-01 24 -0.11884E-01 25 -0.13578E-01 26 -0.15425E-01 27 -0.17433E-01 28 -0.19607E-01 29 -0.21954E-01 30 -0.24481E-01 31 -0.27194E-01 32 -0.30100E-01 33 -0.33205E-01 34 -0.36516E-01 35 -0.40039E-01 36 -0.43781E-01 37 -0.47749E-01 ***** POST1 NODAL DEGREE OF FREEDOM LISTING ***** LOAD STEP= 0 SUBSTEP= 1 TIME= 1.0000 LOAD CASE= 0 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM NODE UX 38 -0.51948E-01 39 -0.56385E-01 40 -0.61066E-01 41 -0.65999E-01 42 -0.71189E-01 43 -0.76642E-01 44 -0.82366E-01 45 -0.88366E-01 46 -0.94648E-01 47 -0.10122 48 -0.10809 49 -0.11525 50 -0.12273 51 -0.13052

MAXIMUM ABSOLUTE VALUES NODE 2 VALUE -0.13863

DEC

DMF

Exemplo 2: Análise da carga crítica de uma coluna engastada-livre

Nonlinear buckling analysis is more accurate than eigenvalue analysis because it employs non-linear, large-deflection, static analysis to predict buckling loads. Its mode of operation is very simple: it gradually increases the applied load until a load level is found whereby the structure becomes unstable (ie. suddenly a very small increase in the load will cause very large deflections). The true non-linear nature of this analysis thus permits the modeling of geometric imperfections, load perterbations, material nonlinearities and gaps. For this type of analysis, note that small off-axis loads are necessary to initiate the desired buckling mode.

i. Seção: 10x10 mm ii. Cross-sectional area AREA: 100

iii. Area moment of inertia IZZ: 833.333iv. Total Beam Height HEIGHT: 10v. Young's modulus EX: 200000

vi. Poisson's Ratio PRXY: 0.3

Deformada:

Deflexão UY

Deflexão UX

Deflexão versus carregamento