The Shell ele ment co or di nate an gle, ang, is used to de fine ele ment ori en ta tions that are dif fer ent from the de fault ori en ta tion. It is the an gle through which the lo cal 1 and 2 axes are ro tated about the posi tive lo cal 3 axis from the de fault ori en ta tion. The ro ta tion for a posi tive value of ang ap pears coun ter clock wise when the lo cal +3 axis is point ing to ward you.
For hori zon tal ele ments, ang is the an gle be tween the lo cal 2 axis and the hori zon tal +Y axis. Oth er wise, ang is the an gle be tween the lo cal 2 axis and the ver ti cal plane con tain ing the lo cal 3 axis. See Figure 32 (page 134) for ex am ples.
Advanced Local Coordinate System
By de fault, the ele ment lo cal co or di nate sys tem is de fined us ing the ele ment co or - di nate an gle meas ured with re spect to the global +Z and +Y di rec tions, as de scribed in the pre vi ous topic. In cer tain mod el ing situa tions it may be use ful to have more con trol over the speci fi ca tion of the lo cal co or di nate sys tem.
This topic de scribes how to de fine the ori en ta tion of the tan gen tial lo cal 1 and 2 axes, with re spect to an ar bi trary ref er ence vec tor when the ele ment co or di nate an -
gle, ang, is zero. If ang is dif fer ent from zero, it is the an gle through which the lo cal 1 and 2 axes are ro tated about the posi tive lo cal 3 axis from the ori en ta tion de ter - mined by the ref er ence vec tor. The lo cal 3 axis is al ways nor mal to the plane of the ele ment.
For more in for ma tion:
• See Chap ter “Co or di nate Sys tems” (page 11) for a de scrip tion of the con cepts and ter mi nol ogy used in this topic.
134
Advanced Local Coordinate SystemZ X Y 45° 90° –90° 3
For all elements, Axis 3 points outward,
toward viewer 1 2 1 2 1 2 1 2 3 3 3
Top row: ang = 45° 2nd row: ang = 90° 3rd row: ang = 0° 4th row: ang = –90°
Figure 32
• See Topic “Lo cal Co or di nate Sys tem” (page 132) in this Chap ter.
Reference Vector
To de fine the tan gen tial lo cal axes, you spec ify a ref er ence vec tor that is par al lel to the de sired 3-1 or 3-2 plane. The ref er ence vec tor must have a posi tive pro jec tion upon the cor re spond ing tan gen tial lo cal axis (1 or 2, re spec tively). This means that the posi tive di rec tion of the ref er ence vec tor must make an an gle of less than 90° with the posi tive di rec tion of the de sired tan gen tial axis.
To de fine the ref er ence vec tor, you must first spec ify or use the de fault val ues for: • A pri mary co or di nate di rec tion pldirp (the de fault is +Z)
• A sec on dary co or di nate di rec tion pldirs (the de fault is +Y). Di rec tions pldirs and pldirp should not be par al lel to each other un less you are sure that they are not par al lel to lo cal axis 3
• A fixed co or di nate sys tem csys (the de fault is zero, in di cat ing the global co or - di nate sys tem)
• The lo cal plane, lo cal, to be de ter mined by the ref er ence vec tor (the de fault is 32, in di cat ing plane 3-2)
You may op tion ally spec ify:
• A pair of joints, plveca and plvecb (the de fault for each is zero, in di cat ing the cen ter of the ele ment). If both are zero, this op tion is not used
For each ele ment, the ref er ence vec tor is de ter mined as fol lows:
1. A vec tor is found from joint plveca to joint plvecb. If this vec tor is of fi nite length and is not par al lel to lo cal axis 3, it is used as the ref er ence vec tor Vp 2. Oth er wise, the pri mary co or di nate di rec tion pldirp is evalu ated at the cen ter of
the ele ment in fixed co or di nate sys tem csys. If this di rec tion is not par al lel to lo cal axis 3, it is used as the ref er ence vec tor Vp
3. Oth er wise, the sec on dary co or di nate di rec tion pldirs is evalu ated at the cen ter of the ele ment in fixed co or di nate sys tem csys. If this di rec tion is not par al lel to lo cal axis 3, it is used as the ref er ence vec tor Vp
4. Oth er wise, the method fails and the analy sis ter mi nates. This will never hap pen if pldirp is not par al lel to pldirs
A vec tor is con sid ered to be par al lel to lo cal axis 3 if the sine of the an gle be tween them is less than 10-3
.
The use of the co or di nate di rec tion method is il lus trated in Figure 33 (page 136) for the case where lo cal = 32.
A spe cial op tion is avail able for back ward com pati bil ity with pre vi ous ver sions of the pro gram. If pldirp is set to zero, the ref er ence vec tor Vp is di rected from the mid point of side j1-j3 to the mid point of side j2-j4 (or side j2-j3 for the tri an gle). This is il lus trated in Figure 30 (page 130), where the ref er ence vec tor would be iden ti cal to lo cal axis 1. With this op tion, the ori en ta tion of the tan gen tial lo cal axes is very de pend ent upon the mesh used.