By de fault each Plane el e ment in cludes four in com pat i ble bend ing modes in its stiff ness for mu la tion. These in com pat i ble bend ing modes sig nif i cantly im prove the bend ing be hav ior in the plane of the el e ment if the el e ment ge om e try is of a rect - an gu lar form. Im proved be hav ior is ex hib ited even with non-rect an gu lar ge om e try. If an el e ment is se verely dis torted, the in clu sion of the in com pat i ble modes should be sup pressed. The el e ment then uses the stan dard isoparametric for mu la tion. In - com pat i ble bend ing modes may also be sup pressed in cases where bend ing is not im por tant, such as in typ i cal geotechnical 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 Plane 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.
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Mass 3 (Element, Material) a a 1 (Element) 1 (Material) 2 (Element) 2 (Material) Figure 37The to tal mass of the ele ment is equal to the in te gral over the plane of the ele ment of the mass den sity, m, mul ti plied by the thick ness, th. 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) even when the ele ment con trib utes stiff ness to only two of these de grees of free dom.
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 Plane ele ment, the self- weight is a force that is uni formly dis trib uted over the plane of the ele ment. The mag ni tude of the self- weight is equal to the weight den sity, w, mul ti - plied by the thick ness, th.
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 “Thick ness” (page 153) in this Chap ter for the defi ni tion of th. • See Topic “Self- Weight Load” (page 245) in Chap ter “Load Cases.”
Gravity Load
Grav ity Load can be ap plied to each Plane 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 155) in this Chap ter for the defi ni tion of self- weight for the Plane 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 three or four side faces of the Plane ele ment. The defi ni tion of these faces is shown in Figure 30 (page 130). Sur face pres sure al ways acts nor mal to the face. Posi tive pres sures are di rected to ward the in te rior of the ele ment.
The pres sure may be con stant over a face or in ter po lated from val ues given at the joints. The val ues given at the joints are ob tained from Joint Pat terns, and need not be the same for the dif fer ent faces. Joint Pat terns can be used to eas ily ap ply hy dro - static pres sures.
The pres sure act ing on a side is mul ti plied by the thick ness, th, in te grated along the length of the side, and ap por tioned to the two or three joints on that side.
See Chap ter “Load Cases” (page 241) for more in for ma tion.