Zero subtraction from a Matrix in Matlab

A=[2 1 0 7 0 1 0 3 4 8 7 5 0 2];
A(A==0)=[];

Difference between Continuum Damage Mechanics approach and Fracture Mechanics approach (zz)

 

http://imechanica.org/node/2988

In Continuum Damage Mechanics (CDM), cracks occur at a level and number such that they are modeled as smeared out continuously. In Fracture Mechanics (FM) some small number of cracks are considered which are of size of the scale of interest. To generalise, CDM is useful to model the degradation of a mechanical body leading up to macrocracks and FM is useful for modeling the mechanical body after cracks on the scale of the structure have formed.

In CDM, the engineer imagines that some of the material has become ineffective at resisting loads. For example, if 20% of the material in the cross-section of a bar has become ineffective at resisting loads and the remaining 80% of the material still behaves as the material normally would, CDM would analyse as though the bar is a normal bar with a full area of material with 80% of the strength and stiffness of the real material. This is extended to multiple dimensions.

In FM, some crack is analysed. Its geometry is important and affects the behaviour of the structure. Traditionally small numbers (think on the order of one) of cracks could be analysed, though modern computational methods allow the engineer to model many cracks. Often the cracks in FM are too large to model as though they were smeared out.

I hope this has helped you with your understanding somewhat.

Rainflow Counting Technical Background

Rainflow counting is a process to obtain equivalent constant amplitude cycles. Its name comes from the original description from the Japanese researchers Matsuiski and Endo where they describe the process in terms of rain falling off a pagoda style roof. A more insightful description based on cyclic plasticity is usually used to explain the method.

A	10
B	-8
C	5
D	-10
E	-3
F	-9
G	6
H	4
I	10

In the figure above a simple loading history ( points A - I ) is plotted vertically so that it resembles a Japanese pagoda. The resulting deformation, stresses and strains, is plotted directly below the loading history. In the lower part of the figure, four cycles are easily identified. One large overall cycle, one intermediate cycle in the center of the plot, and two smaller cycles. Each cycle has its own strain range and mean stress. From a deformation viewpoint the process proceeds as follows. Start at A, the maximum strain, and unload the material to B. Then reload to point C and unload to D. When the material reaches the strain at point B during the unloading from C to D the material remembers its prior deformation and deforms along a path from A to D as if the event C-D never happened. This is better illustrated in the next part of the loading. Load from D to E and unload to F. Now load from F to G. When the material reaches the strain at point E during the loading from F to G the material remembers its prior deformation and deforms along a path from D to G as if the event E-F never happened. The same process occurs for G-H.

Rainflow counting will identify four cycles, A-D-I, B-C-B, E-F-E and G-H-G. Rainflow counting identifies the major load excursions, for example D to I, and treats subcycles like E-F and G-H as interruptions to the overall loading event D-I

cycles mean amplitude

b-c 1.0000 -1.5000000000 6.5000000000

e-f 1.0000 -6.0000000000 3.0000000000

g-h 1.0000 5.0000000000 1.0000000000

a-d 0.5000 0.0000000000 10.0000000000

d-i 0.5000 0.0000000000 10.0000000000