William R. Derrick

Structure-material relations in the buckling problem of asymmetric composite columns

Abstract The paper examines the effects of material composition and properties on the non-linear buckling response of asymmetric laminated structures. The problem is studied through the analysis of asymmetric laminated columns composed of an arbitrary number of different material layers. The non-linear buckling behavior of the columns subjected to combined compression and bending is examined depending on parameters such as the number, orientation and stacking sequence of the layers that make up the laminate. The analysis demonstrates that, under certain conditions, asymmetric laminated columns subjected to combined compression and bending exhibit bifurcation. In such cases, the onset of lateral deformations of the columns is delayed until the applied moment–force system attains its critical value. Based on the analytical solution of the non-linear buckling problem under consideration, the potentials for maximizing the critical load and controlling the buckling characteristics of laminated composites through tailoring their material properties are analyzed.

Dynamics of Lotka-Volterra systems with exploitation

This paper deals with some unusual dynamics that occur when two competing populations are exploited by a discriminating consumer. Individual consumers feed to satiation in proportion to a relative preference for, and the relative abundance of, the resource species. Under preferential exploitation, stable equilibria of competing populations generally vanish through saddle-node bifurcations at substantial population levels. Further, subcritical Hopf bifurcations can occur through saddle connections or homoclinic orbit bifurcations, triggering stable periodic oscillations under constant exploitation.

Bray-Liebhafsky Oscillations

Summary. A system describing an oscillating chemical reaction (known as a Bray—Liebhafsky oscillating reaction) is considered. It is shown that large amplitude oscillations arise through a homoclinic bifurcation and vanish through a subcritical Hopf bifurcation. An approximate locus of points corresponding to the homoclinic orbit in a parameter space is calculated using a variation of the Bogdanov—Takens—Carr method. A special feature of the problem is related to the fact that nonlinear terms in the equations contain square and cubic roots of expressions depending on the unknowns. For a particular model considered it is possible to obtain most of the results analytically.

Buckling resistance of composite wind turbine blades

The paper concerns the buckling analysis and optimization of composite wind turbine blade substructures. Attention is focused on the compression response of a laminated web element under the action of combined compression and bending. The study is based on general assumptions regarding the properties, number and stacking sequence of the layers. Buckling and postbuckling responses of the web element are studied, and the critical buckling condition is obtained based on nonlinear analysis. It is shown that the buckling resistance of the web element can be enhanced by tailoring the material composition and properties of the laminate.

Continued Fractions, Chebychev Polynomials, and Chaos

For arbitrary t1, (2) is a one-parameter family of discrete dynamical systems, and it is in this context that we will speak of chaos in Sections 6 and 7. If you have a calculator or computer, you can readily check that S2(1) = 1 and S2(0.98)= 1.14142135624.... These answers can also be obtained by assuming convergence in (2) to t and solving the quadratic t2 = 2t a. In general, one can easily prove the following result.