Approximate and refined analysis methods - Computational Analysis and Design of Bridge Structures - page 37

Area elements —Area elements in the finite element analysis also include
two types, elements with in-plane effects only and elements with both
in-plane and out-of-plane effects. The in-plane element, which is often
referred as membrane element , may be either plane stress or plane strain
element. Each node of a membrane element has two degrees of freedom
( u , v ) in the element plane. It has been used less than the second plate element
type, which is used to simulate not only in-plane (membrane) action with
degrees of freedom ( u , v ) but also plate bending (flexural) action with an
additional three degrees of freedom ( w , θ x , θ y ) at each node. This type of
combined plate element is often referred to as plane shell element , to dif-
ferentiate a pure bending plate element. Plane shell element is so called as
it can be used to assembe a true shell structure. As shown in Figure 2.18,
these area elements may be triangular or rectangular in shape. The shell
elements can be used to model many parts of bridge structures. Figure 2.19
shows the nodes and elements of a deck modeled by shell elements, and
Figure 2.20 illustrates an actual structure with its idealized model.

z

x

ω

ω

Membrane-flexural
element

y

μ

θ x

θ x

μ

(Five degrees of freedom
per node)

θ y

θ y

υ

υ

Figure 2.18 Degrees of freedom of a plane shell element.

1 13 25 37 49 61 73 85 97 109 121 133 145

1 2 3 4 5 6 7 8 9 10 11 12

14 26 74 110 146

2

13 24

15 27 75 111 147

3

25

36

16 28 76 112 148

4

37 48

17 29 77 113 149

5

49 60

18 30 78 114 150

6

61 62 63 64 65 66 67 68 69 70 71 72

7

19 31 43 55 67 79 91 103 115 127 139 151

Figure 2.19 Finite element example of nodes and elements (numbers in circles) of a slab
model.