Civil engineering Finite Elements questions Consider the 2-noded element shown in Fig. 1 that has nodes at x = −1 and x = +1. (a) Write the shape functions N1(x) and N2(x). (b) Show that the shape functions satisfy the Kronecker delta property, i.e., Ni(x) = 1 at node i and zero at the other node(s). (c) Show that the shape functions satisfy the ”Rigid Body mode(s)” condition, i.e., N1(x)+ N2(x) = 1. (d) Show that the shape functions satisfy the ”Constant Strain state(s)” condition, i.e., N1(x)x1 + N2(x)x2 = x.
Civil engineering Finite Elements questions Consider the 2-noded element shown in Fig. 1 that has nodes at x = −1 and x = +1. (a) Write the shape functions N1(x) and N2(x). (b) Show that the shape functions satisfy the Kronecker delta property, i.e., Ni(x) = 1 at node i and zero at the other node(s). (c) Show that the shape functions satisfy the ”Rigid Body mode(s)” condition, i.e., N1(x)+ N2(x) = 1. (d) Show that the shape functions satisfy the ”Constant Strain state(s)” condition, i.e., N1(x)x1 + N2(x)x2 = x.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Civil engineering Finite Elements questions
Consider the 2-noded element shown in Fig. 1 that has nodes at x = −1 and
x = +1.
(a) Write the shape functions N1(x) and N2(x).
(b) Show that the shape functions satisfy the Kronecker delta property, i.e., Ni(x) = 1 at
node i and zero at the other node(s).
(c) Show that the shape functions satisfy the ”Rigid Body mode(s)” condition, i.e., N1(x)+
N2(x) = 1.
(d) Show that the shape functions satisfy the ”Constant Strain state(s)” condition, i.e.,
N1(x)x1 + N2(x)x2 = x.
Transcribed Image Text:1
X = -1
Figure 1: Problem 1.
2
X = +1
X
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