Answer concisely: (a) Element stiffness matrices [ k ] are always nonsingular—true or false? Make your choice and justify. (b) The strain energy in a structure, U = ½ QT K Q is always 7 0 for any Q ,...

Answer concisely:

(a) Element stiffness matrices [ k ] are always nonsingular—true or false? Make your choice and justify. (b) The strain energy in a structure, U = ½ QT K Q is always 7 0 for any Q , provided _____________________________________________ (Fill in the blanks.) (c) A finite element model of a rod is given a displacement Q = [1, 1, . . . , 1] T . The associated strain energy U = ½ QT K Q equals zero. What can you conclude regarding the stiffness matrix K ? (d) Consider a rod fixed at its ends, x = 0 and x = 1, respectively. Is the axial displacement field u = ( x-1) 2 “kinematically admissible” ?