Quadrilateral isoparametric elements

The previous section used the constant strain three-noded element to solve Poisson s equation with steady-state as well as transient terms. The same problems, as well as any field problems such as stress-strain and the flow momentum balance, can be formulated using isoparametric elements. With this type of element, the same (as the name suggests) shape functions used to represent the field variables are used to interpolate between the nodal coordinates and to transform from the xy coordinate system to a local element coordinate system. The first step is to discretize the domain presented in Fig. 9.12 using the isoparametric quadrilateral elements as shown in Fig. 9.15. 

Fig. 13.4 (a) Eight-node quadrilateral isoparametric plane stress element (b) embedded reinforcement element... 

The concrete is modeled by eight-node quadrilateral isoparametric plane stress element CQ16M as shown in Fig. 13.4a. The rebar and stirrups are modeled as embedded reinforcement elements with perfect bond between rebar and concrete. The rebar embedded model is shown in Fig. 13.4b. 

Boundary conditions were kept the same as in the actual test of beam-column joints, Fig. 13.20 shows the bottom end of the column surface, constrained in the X and Y direction. The top end of the column is constrained in the X-direction and free in the Y-direction due to downward axial force (150 KN). Near the tip of the free end of the beam, the point is constrained in the y direction because the loading method is displacement control. All the specimens were modeled with eight-node quadrilateral isoparametric plane stress element CQ16M with embedded steel (Fig. 13.21). 

Figure 2.17 Isoparametric mapping of an irregular quadrilateral element wilJi straight sides...

Solution of Field Problems Using Isoparametric Quadrilateral Elements. 

Figure 9.15 Finite element mesh using isoparametric quadrilateral elements for the domain...

Figure 9.16 Isoparametric quadrilateral element in the xy-coordinate system.

The DDM has been extended to the analysis of SFSI systems. This extension required development and implementation of response sensitivity algorithms for 2-dimensional (quadrilateral) and 3-dimensional (brick) isoparametric finite elements, soil materials (such as the pressure-independent multi-yield surface plasticity model, see Prevost 1977, Gu et al. 2008b, c) and handling of multipoint constraints (Gu et al. 2008a) required for properly connecting finite elements used in modelling the soil domain with the ones used for the superstructure model (such as frame elements). A benchmark... 

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