Mechanical buckling load

Structural mechanics analyses are used to determined design variables such as displacements, forces, vibrations, buckling loads, and dynamic responses, including application of corresponding special areas of structural mechanics for simple structural elements. General purpose finite element programs such as NASTRAN are used for the structural analysis of complex structural shapes, large structures made from simple structural elements. And structural parts made from combinations of simple elements such as bars, rods and plates. 

Plastic composite mechanics in conjunction with structural mechanics can be used to derive explicit equations for the structmal response of simple structural elements. These explicit expressions can then be used to perform parametric studies (sensitivity analyses) to assess the influence of the hybridization ratio on structural response. For example the structural response (behavior variables) equations for maximum deflection, buckling load and frequency of a simply supported beam made from intraply hybrids are summarized in Figure 6.7 Flexural modulus is used to determine the maximum deflection, buckling load, and frequency of a simple supported beam made from intraply hybrids. 

Waszczyszyn, Z. Bartczak, M. 2002. Neural prediction of buckling loads of cylindrical shells with geometrical imperfections. International Journal of Non-Linear Mechanics 31 763-775. 

The deformation mechanisms of a honeycomb were analyzed in detail in [8]. Cell deformations by cell wall bending and buckling were eonsidered for the elastics extension or compression of the honeyeomb. The elastie collapse or buckling occurs when the load exceeds the Euler buckling load and the elastic collapse stress, cjei, can be expressed as ... 

In many cases, a product fails when the material begins to yield plastically. In a few cases, one may tolerate a small dimensional change and permit a static load that exceeds the yield strength. Actual fracture at the ultimate strength of the material would then constitute failure. The criterion for failure may be based on normal or shear stress in either case. Impact, creep and fatigue failures are the most common mode of failures. Other modes of failure include excessive elastic deflection or buckling. The actual failure mechanism may be quite complicated each failure theory is only an attempt to explain the failure mechanism for a given class of materials. In each case a safety factor is employed to eliminate failure. 

We have discussed the value of struts or columns in structural mechanics and described their linear elastic properties. They have another characteristic that is not quite so obvious. When columns are subject to a compressive load, they are subject to buckling. A column will compress under load until a critical load is reached. Beyond this load the column becomes unstable and lateral deformations can grow without bound. For thin columns, Euler showed that the critical force that causes a column to buckle is given by... 

If gapping is too narrow and cannot accommodate the swelling, this situation leads to buckling, distortions, cracking, and other types of failure (Fig. 12.4-12.9) Clearly, for such distortions and mechanical failure of composite deck boards, a significant pressure/load should have been developed. It was determined that the... 

The alumina scale shown in Figs. 7c and d failed certainly by the buckling mechanism. Within the spalled regions on the specimen surface, large interfacial voids were detected which represent interfacial flaws where the scale buckles during scale loading. A mechanical stability analysis yields the critical equi-biaxial stress, orh. when buckling occurs [7]... 

Li and Chou [73,74] have reported a multiscale modeling of the compressive behavior of CNT/polymer composites. The nanotube is modeled at the atomistic scale, and the matrix deformation is analyzed by the continuum FEM. The nanotube arrd polymer matrix are assttmed to be bonded by vdW interactions at the interface. The stress distributiorrs at the nanotube/polymer interface under isostrain and isostress loading conditiorrs have been examined. They have used beam elements for SWCNT using molectrlar structural mechanics, truss rod for vdW links and cubic elements for matrix. The rule of mixtrrre was used as for comparision in this research. The buckling forces of nanotube/polymer composites for different nanotube lengths and diameters are computed. The results indicate that continuous nanotubes can most effectively enhance the composite buckling resistance. 

Extensive physical and mechanical analysis of the materials, forces, and loads involved has been undertaken to understand the amazing resistance of the long mosquito labium to buckling. Estimates of the critical axial load before buckling (Per) have been based on the Euler equation in the following form ... 

Similar to beam buckling, membrane buckling is another important mechanism for thermal expansion microvalves. To investigate the bending of a membrane when heat is added to it. Fig. lb illustrates the principle of the thermal buckling of a square membrane. Considering a uniform compression condition across the membrane (i.e., the compressive stress is constant, Sx = Sy = S), the membrane buckles transversally without any additional external load when the compressive stress gradually increases with temperature and exceeds the critical stress, Sa- The critical stress is defined as... 

---