The ma te rial lo cal co or di nate sys tem and the el e ment (Property) lo cal co or di nate sys tem need not be the same. The ma te rial co or di nate sys tem is ori ented with re - spect to the el e ment co or di nate sys tem us ing the three an gles a, b, and c ac cord ing to the fol low ing pro ce dure:
• The ma te rial sys tem is first aligned with the el e ment sys tem; • The ma te rial sys tem is then ro tated about its +3 axis by an gle a;
• The ma te rial sys tem is next ro tated about the re sult ing +2 axis by an gle b; • The ma te rial sys tem is lastly ro tated about the re sult ing +1 axis by an gle c; This is shown in Figure 43 (page 181). These an gles have no ef fect for iso tro pic ma te rial prop er ties since they are in de pend ent of ori en ta tion.
See Topic “Lo cal Co or di nate Sys tem” (page 68) in Chap ter “Ma te rial Prop erties” for more in for ma tion.
Incompatible Bending Modes
By de fault each Solid ele ment in cludes nine in com pati ble bend ing modes in its stiff ness for mu la tion. These in com pati ble bend ing modes sig nifi cantly im prove
the bend ing be hav ior of the ele ment if the ele ment ge ome try is of a rec tan gu lar form. Im proved be hav ior is ex hib ited even with non- rectangular ge ome try. If an ele ment is se verely dis torted, the in clu sion of the in com pati ble modes should be sup pressed. The ele ment then uses the stan dard iso para met ric for mu la tion. In - com pati ble bend ing modes may also be sup pressed in cases where bend ing is not im por tant, such as in typi cal geo tech ni cal prob lems.
Mass
In a dy namic analy sis, the mass of the struc ture is used to com pute in er tial forces. The mass con trib uted by the Solid ele ment is lumped at the ele ment joints. No in er - tial ef fects are con sid ered within the ele ment it self.
The to tal mass of the ele ment is equal to the in te gral of the mass den sity, m, over the vol ume of the ele ment. The to tal mass is ap por tioned to the joints in a man ner that is pro por tional to the di ago nal terms of the con sis tent mass ma trix. See Cook, Malkus, and Ple sha (1989) for more in for ma tion. The to tal mass is ap plied to each of the three trans la tional de grees of free dom (UX, UY, and UZ).
Mass
181
1 (Element) 1 (Material) 2 (Element) 2 (Material) 3 (Element) 3 (Material) a a a b b b c c cRotations are performed in the order
a-b-c about the axes shown.
Figure 43
For more in for ma tion:
• See Topic “Mass Den sity” (page 74) in Chap ter “Ma te rial Prop er ties.” • See Chap ter “Anal y sis Cases” (page 255).
Self-Weight Load
Self- Weight Load ac ti vates the self- weight of all ele ments in the model. For a Solid ele ment, the self- weight is a force that is uni formly dis trib uted over the vol ume of the ele ment. The mag ni tude of the self- weight is equal to the weight den sity, w. Self- Weight Load al ways acts down ward, in the global –Z di rec tion. You may scale the self- weight by a sin gle scale fac tor that ap plies equally to all ele ments in the struc ture.
For more in for ma tion:
• See Topic “Weight Den sity” (page 75) in Chap ter “Ma te rial Prop er ties” for the defi ni tion of w.
• See Topic “Self- Weight Load” (page 245) in Chap ter “Load Cases.”
Gravity Load
Grav ity Load can be ap plied to each Solid ele ment to ac ti vate the self- weight of the ele ment. Us ing Grav ity Load, the self- weight can be scaled and ap plied in any di - rec tion. Dif fer ent scale fac tors and di rec tions can be ap plied to each ele ment. If all ele ments are to be loaded equally and in the down ward di rec tion, it is more con ven ient to use Self- Weight Load.
For more in for ma tion:
• See Topic “Self- Weight Load” (page 182) in this Chap ter for the defi ni tion of self- weight for the Solid ele ment.
• See Topic “Grav ity Load” (page 246) in Chap ter “Load Cases.”
Surface Pressure Load
The Sur face Pres sure Load is used to ap ply ex ter nal pres sure loads upon any of the six faces of the Solid ele ment. The defi ni tion of these faces is shown in Figure 40