Large deflection response

If the magnitude of the center point deflection of the film wq increases to values on the order of film thickness h, then the potential arises for generation of significant membrane stress in the film due to transverse deflection (in addition to any residual membrane stress which may be present in the film prior to deflection). As in the case of film buckling, the von Karman plate theory provides a useful and effective framework for describing response with center point deflection wq of magnitude equal to several times the film thickness. In the present case, the von Karman equations reduce to the pair of ordinary differential equations 

The parameter to is the spatially uniform membrane tension in the film its value prior to application of the pressure p is UjJii where a a is the uniform residual stress. The six boundary conditions in (5.62) yield values for the five integration constants which arise from solution of the differential equations and for the membrane stress to following application of the pressure p. 

For the time being, consider the case of no initial residual stress, that is, (7m = 0. For this case, the relationship between the membrane stress to in the film and the applied pressure p that is implied by (5.61) and (5.62) is given by 

The energy release rate G o) for spread of the zone of application of the pressure is again given by (5.38). In the present instance, the membrane 

---

Derivation of the corresponding result for large deflection response is left is an exercise. 

In designing axi-symmetric shell structures such as large-type cooling towers, it is necessary to predict the vibration responses to various external forces. The authors describe the linear vibration response analysis of axi-symmetric shell structures by the finite element method. They also analyze geometric nonlinear (large deflection) vibration which poses a problem in thin shell structures causes dynamic buckling in cooling towers. They present examples of numerical calculation and study the validity of this method. 11 refs, cited. 

Multiple valves have been constructed on a PDMS valve control layer (see Figure 3.27) [167]. Multilayer soft lithography has been used to generate the valve control layer (4 mm thick for strength) plus a fluid layer (40 pm thick) on PDMS. The small Young modulus ( 750 kPa) of PDMS allows a large deflection (1 mm) to be produced using a small actuation force ( lOOkPa on a 100- x 100-pm valve area). The response time is on the order of 1 ms. Round channels were... 

In view of the large lateral deflection responses of the fire-exposed specimens, shown in Figure 8.12, second-order deformations had to be taken into account in the modeling, and for their quantification, the post-fire Euler budding load had first to be determined. The latter was estimated by Eq. (7.12), where EI t) is the effective bending stiffness of the specimen after a fire-exposure duration of t, and L is the height of the specimens (2825 mm). 

The equipment required for slow strain-rate testing is simply a device that permits a selection of deflection rates whilst being powerful enough to cope with the loads generated. Plain or precracked specimens in tension may be used but if the cross-section of these needs to be large or the loads high for any reason, cantilever bend specimens with the beam deflected at appropriate rates may be used. It is important to appreciate that the same deflection rate does not produce the same response in all systems and that the rate has to be chosen in relation to the particular system studied (see Section 8.1). 

The capacity of a member to deform significantly and absorb energy is dependent on the ability of the connections to maintain strength throughout the response. If connections become unstable at large responses, catastrophic failure can occur. The resistance will drop thereby increasing deflections. Connections often control blast capacity for structures which have been designed for conventional loads only. 

---