Elastic foundation
Coefficient of subgrade reaction is in MPa/m or N/m^2/m. There is not document explaining how to convert subgrade reaction to a single spring stiffness to support truss structure. By chance, I chose ks = 99461 N/m as an equivent spring constant and the result of the displacement is similar to the calculation in Nam Il Kim, 2013. I still don’t know how to formulate this model yet. I only doubt that C. V. G. Vllabhan and Y. C. Das, “A refined model for beam on elastic foundations”, 1991, (ref23) use a 1 m x 1 m plate suppor. However, I cannot access this paper from the university profile.
Anyway, below is the result from unit test by vibrating the structure with elastic support and under loading condition
Numerical Tests
1. Rao, 2004, 2D structure, 11 members, 6 nodes
2. Nam Il Kim, 2013, 2D structure, elastic support, 16 members, 8 nodes
3. Nam Il Kim, 2013, 3D structure, elastic support, 36 members, 12 nodes
Accuracy
Case 1 Rao 2D
a. 0.99999994 0.99999994 0.99999992 0.99999998 0.99999928 0.99999963 0.99999997 0.99999697 0.99999718 0.99999996 0.99999987
b. 0.99999950 0.99999737 0.30003350 0.99999970 0.99998897 0.70000161 0.99999973 0.99999967 0.99999999 0.99999310 0.99999987
c. 0.99999205 0.99999842 0.99999323 0.99998044 0.99999845 0.99999802 0.99999953 0.99999993 0.99999934 0.00000371 0.99999806
Case 2 Kim 2D
a. 0.99999902 0.99999995 0.99999968 0.99999813 0.99999993 0.99999996 1.00000000 0.99999910 0.99999761 0.99999985 0.99999973 0.99999946 0.99999881 0.99999398 0.99999992 0.99999913
b. 0.99999997 0.99999978 0.99999717 0.99999774 0.99999845 0.99999917 0.99999989 0.99999829 0.29999817 0.99999999 0.99999729 0.99999995 1.00000000 0.99999985 0.99999968 0.99999996
c. 0.99999778 0.99999992 0.99999660 0.99999521 0.40004479 0.99999412 0.99999997 0.99999857 0.99999843 0.99999991 0.99997469 0.99999964 0.29999698 0.99999427 0.99999978 0.99999572
Case 3 Kim 3D
a. 0.99999995 0.99999995 0.99999994 0.99999790 0.99999934 1.00000000 0.99999980 0.99999998 0.99999938 0.99999962 0.99999999 0.99999999 0.99999966 0.99999999 0.99999992 0.99999954 0.99999915 0.99999926 0.99999935 0.99999991 0.99999968 0.99999981 0.99999993 0.99999957 0.99999966 0.99999660 0.99999954 0.99999977 0.99999901 0.99999998 0.99999795 0.99999897 0.99999976 0.99999998 0.99999996 0.99999858
b. 0.99999899 0.99999946 0.99999985 0.99999969 0.99998630 0.99998776 0.99999929 0.99999988 0.99999915 0.99999995 0.99999809 0.99999988 0.40005280 0.99999993 0.99999970 0.99999999 0.99998697 0.99999273 0.99999987 0.99999917 0.99999693 0.99999937 0.99999978 0.99999952 0.99999789 0.99999994 0.99999859 0.99999999 0.99999992 0.99999990 0.99999976 0.99999988 0.99999792 0.99999981 0.99999978 1.00000000
c. 0.30000695 0.99999987 0.99999980 0.99999941 0.99999868 0.99999986 0.99999985 0.99999061 0.99999959 0.99999948 0.99999992 0.99999970 0.99999999 0.99999975 0.99999973 0.99999995 0.99999954 0.99999953 0.99999994 0.99999934 0.49938421 0.99999465 0.99999935 0.99999981 0.99999889 1.00000000 0.99999924 0.99999990 0.99999539 0.99999994 0.99999995 0.99999953 0.99999994 0.99999961 0.99999973 0.99999493