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Podatki

Ključna je simetrija tenzorja napetosti [σij] . To upoštevamo že pri podatkih.

In[2]:=

σij = {{σxx, σxy, σxz}, {σxy, σyy, σyz}, {σxz, σyz, σzz}} ; ea = {eax, eay, eaz} ; eb   = {ebx, eby, ebz} ;

Napetostni vektor v ravnini z normalo e_a

In[5]:=

σa = σij . ea

Out[5]=

{eax σxx + eay σxy + eaz σxz, eax σxy + eay σyy + eaz σyz, eax σxz + eay σyz + eaz σzz}

Napetostni vektor v ravnini z normalo e_b

In[6]:=

σb = σij . eb

Out[6]=

{ebx σxx + eby σxy + ebz σxz, ebx σxy + eby σyy + ebz σyz, ebx σxz + eby σyz + ebz σzz}

Dokaz (projekcija σ_a na smer e_b - projekcija σ_b na smer e_a = 0)

In[7]:=

σa . eb - σb . ea // Simplify

Out[7]=

0

In[8]:=

Clear[σij, ea, eb, σa, σb, σxx, σxy, σxz, σxy, σyy, σyz, σxz, σyz, σzz, eax, eay, eaz, ebx, eby, ebz ] ;

Created by Mathematica  (October 30, 2003)