{"responseHeader":{"status":0,"QTime":7,"params":{"q":"{!q.op=AND}id:\"103626\"","hl":"true","hl.simple.post":"","hl.fragsize":"5000","fq":"!embargo_tdt:[NOW TO *]","hl.fl":"ocr_t","hl.method":"unified","wt":"json","hl.simple.pre":""}},"response":{"numFound":1,"start":0,"docs":[{"file_name_t":"Thingvold-Elastic_and_Plastic.pdf","thumb_s":"/98/11/981190055ac689017932967ddf2a09a7056c77ec.jpg","oldid_t":"compsci 11739","setname_s":"ir_computersa","restricted_i":0,"format_t":"application/pdf","modified_tdt":"2016-05-26T00:00:00Z","file_s":"/23/9a/239a60c7994bab086cf3124f4fbb8bb9191a56f8.pdf","title_t":"Page 58","ocr_t":"46 mass, as in B-spline refinement, to determine appropriate mass values. H the mass values for the points are considered as coefficients for a pair of B-splines, then by maintaining constant coefficients, the sum of the basis functions for the B-splines would remain at 1. This treatment is consistent with the view that the mass is not all contained at the control points but is continuously distributed throughout the surface. For the refinement of hinges, the problem is to consider a series of hinges hooked together where the endpoint of one hinge is the mid point of the next hinge. In the general case, the geometric argument of equation 7.5 is extended by maintaining the sum of the supplements of the equilibrium angles of all the hinges before and after refinement. As in the single hinge refinement, strains are not preserved when this is done. The hinge constants for the hinges at either end of the configuration are modified to maintain a constant force application by those hinges. The hinge constants for interior hinges are modified to obtain a smooth change from one end of the configuration to the other. Unfortunately, the fact that the hinges overlap causes a problem. Hinges apply forces to their endpoints as well as their midpoints. For example, in Figure 7.3, there exists a hinge whose midpoint is P3 • Before refinement, this hinge created a torque about P3 that is turned into a force applied to P2 by dividing the torque by the distance from P2 to P3 • After refinement, this same torque value is now turned into a force applied to P4 by dividing the torque by the distance from P4 to P3 • The applied force has now increased, possibly by as much as 50%. From the definition of a hinge in section 3.3, forces applied to the endpoints of a hinge are also applied to the midp~ints to conserve momentum. Thus, the increased force application to P4 , as a result of refinement, also causes an increase of force applied to P3 • It is not possible for the refined hinges to account for this extra force, since the extra force is applied in a direction not orthogonal to the vector from P3 to P4 •","id":103626,"created_tdt":"2016-05-26T00:00:00Z","parent_i":103685,"_version_":1642982555692040195}]},"highlighting":{"103626":{"ocr_t":[]}}}