CHAPTER 4 77-118
4.4. F INITE E LEMENT A NALYSIS OF C IRCULAR I SOLATOR
4.4.2. Stress and Strain of Circular Isolator
Contour of normal stress S33 corresponding to maximum applied displacement of 60 mm is shown in Fig. 4.32 for both bonded and un-bonded circular isolators. The normal stress S33 acts along Z axis.
(a)Un-bonded circular (b) Bonded circular
Fig. 4.32 Contour of normal stress S33 (kN/m2) in rubber layer of circular isolator at horizontal displacement 60mm (Positive value indicate tension)
The compression load of bonded FREI is carried by central compression core within the overlapping region between the top and bottom faces of isolator. As the lateral deformation increases, area of compression region decreases and peak compression increases in the bonded FREI. The compression in the central core is almost constant
throughout the height of the isolator as can be seen from Fig. 4.32(b). Thus, while the compression is carried through the overlapping region between top and bottom surfaces, the unbalanced moment is carried by tension stresses in the regions outside the overlap.
Vertical load of U-FREI is carried by the central compression core, similar to bonded FREI (Fig. 4.32a). However, the maximum compressive stresses in U-FREIs are developed only in the pressed corner at top and bottom surfaces and the magnitude of peak compression that develop in both isolators are comparable. Further, when an un- bonded isolator is deformed laterally, near end of the loading direction leaves the contact and moves upward causing tension in fibre reinforcement. Similarly, the opposite end of the isolator moves downward and loses contact with the support.
Tension is developed in the region of no contact while other regions remain under compression. However, due to un-bonded application, no tensile stress is transferred to the isolator’s contact support. The unbalanced moments are resisted by the vertical load through offset of the force resultants on the top and bottom surfaces. It may also be noted that the tensile stress S33developed in U-FREI is lesser than those of bonded FREI. Hence, peeling stress demand on the bond between the rubber and fibre reinforcement in case of U-FREI is lesser than that of bonded FREI.
Figs. 4.33(a)-(c) show the distribution of the normalized stress S33/Pn along the horizontal plane of 10th rubber layer located at mid-height of the isolator at lateral displacement of 60mm, 40mm and 20mm. It is observed for bonded isolator that normal compressive stress increases with the increase in the horizontal displacement while the length of compression region decreases. Development of considerable tensile stress is observed in bonded FREI along with the presence of warping effect. However, for un- bonded application, the compressive stress does not vary much with the increase in horizontal displacement and there is no development of tensile stress as well. Further,
peak pressure at the middle of bonded isolator is 52% higher than that of un-bonded isolator corresponding to 60mm horizontal displacement and hence, U-FREIs are less susceptible to Euler buckling as compared to bonded FREI.
(a) 60mm horizontal displacement (b) 40mm horizontal displacement
(c ) 20 mm horizontal displacement
Fig. 4.33 Distribution of normalized S33/Pn in the mid rubber layer rubber layer of circular isolator at 60 mm horizontal displacement
Fig. 4.34 shows the contour of normal stress S11 in the circular isolator corresponding to 60mm lateral displacement. Fig. 4.34(b) indicates that the overlapping region of bonded circular FREI between the top and bottom faces are under biaxial compression.
However, region outside the overlapping zone are under biaxial tension. Similar to the bonded FREI, the central column region of U-FREI also resists the biaxial compression as is evident from Fig. 4.32(a) and 4.34(a). It may be seen from Fig. 4.34(a) and (b) that the peak values of compressive stress in both the isolators are similar; but the compressive stress in central core of U-FREI is much lesser than that of bonded FREI.
-6 -4 -2 0 2
0 0.2 0.4 0.6 0.8 1
Normalized stress S33/Pn
Normalized width of isolator Circular Unbonded Circular Bonded
-6 -4 -2 0 2
0 0.2 0.4 0.6 0.8 1
Normalized stress S33/Pn
Normalized width of isolator Circular Unbonded Circular Bonded
-6 -4 -2 0 2
0 0.2 0.4 0.6 0.8 1
Normalized stress S33/Pn
Normalized width of isolator Circular Unbonded Circular Bonded
Similarly, the peak tensile stress in bonded FREI is significantly lower than for bonded FREI.
(a)Un-bonded circular isolator (b) Bonded circular isolator Fig. 4.34 Contour of normal stress S11 (kN/m2) in rubber layer of isolator at horizontal
displacement 60mm (Positive value indicate tension)
Fig. 4.35(a)-(c) shows the distribution of the normalized stress S11/Pn along the length of 10th rubber layer for 60mm, 40mm and 20mm displacement.
(a) 60mm horizontal displacement (b) 40mm horizontal displacement
(c ) 20 mm horizontal displacement
Fig. 4.35 Distribution of normalized S11/Pn in the mid rubber layer rubber layer of circular isolator at 60 mm horizontal displacement
-6 -4 -2 0 2
0 0.2 0.4 0.6 0.8 1
Normalized stress S11/Pn
Normalized width of isolator Circular Unbonded Circular Bonded
-6 -4 -2 0 2
0 0.2 0.4 0.6 0.8 1
Normalized stress S11/Pn
Normalized width of isolator Circular Unbonded Circular Bonded
-6 -4 -2 0 2
0 0.2 0.4 0.6 0.8 1
Normalized stress S11/Pn
Normalized width of isolator Circular Unbonded Circular Bonded
It is observed that the normal compression stress increases with the increase in the horizontal displacement for bonded FREI, while the same does not vary much for un- bonded application. Development of significant tensile stress in bonded FREI along with the existence of warping effect is observed, while no tensile stress is developed in the un-bonded isolator for the considered range of lateral displacement. Peak pressure in the bonded isolator is 94% higher than that of un-bonded isolator corresponding to 60mm horizontal displacement.
Fig. 4.36 shows the contour plot of shear strain of un-bonded and bonded circular isolator corresponding to 60mm horizontal displacement. Fig. 4.37(a)-(c) illustrates the distribution of shear strain along the rubber plane at mid height of the isolator at different lateral displacements.
(a) Un-bonded circular isolator (b) Bonded circular isolator Fig. 4.36 Contour of shear strain in the rubber layer of circular isolator at horizontal
displacement 60mm
It may be seen from Fig. 4.36 that the peak shear strain values at the mid-section of middle layer of elastomer of both bonded and un-bonded isolators are fairly comparable. It is observed that U-FREI shows uniform shear strain only in the region in contact with top and bottom support, while almost constant shear strain is observed across the width of the bonded isolator. Shear strain in U-FREI is found to decrease from peak to almost zero where the isolator is not in contact with the support. Further, for 60 mm displacement, the shear strain in the isolator can be approximated as
(60mm/104.9mm) ≈0.57. This value is in reasonable agreement with the result shown in Fig. 4.36 and Fig. 4.37.
(a) 60mm horizontal displacement (b) 40mm horizontal displacement
(c ) 20 mm horizontal displacement
Fig. 4.37 Shear strain in the mid rubber layer rubber layer of circular isolator at 60 mm horizontal displacement
4.4.3. Force Displacement Hysteresis Behaviour of Circular Isolator