Nonlinear Effect Of Initial Load On Mechanical Behavior Of Beams

The common theory of the effect of initial load on static and dynamic characteristics and stability of a structure has already been established and well developed since the middle of 20th century. However, basically, it focuses on the effect of axial deformation induced by initial load, and is not much concerned with the effect of flexural deformation induced by initial load. To help understand the effect of initial load on a structure better, this dissertation systematically studies the effect of both axial and flexural deformations induced by initial load on the static and dynamic characteristics of curved as well as straight beams with various restraint conditions, which expands the current nonlinear theory. The major work performed is detailed as follows.1. The governing differential equations are established for straight beams by using energy variation method, considering the effect of flexural deformation induced by initial load. An initial load influence factor is introduced, with its analytical expression given. Through a discussion of various beams (simply-supported beam, beam fixed at the two ends, beam fixed at one end and simply-supported at the other end, and cantilever beam), the effects of key physical parameters, including the magnitude of initial load, sectional inertia moment and inertia radius, span, and restraint conditions, on the initial load influence factor are discussed and the corresponding static and dynamic characteristics are presented.2. The governing differential equations are established for straight beams by using energy variation method, considering the effects of both axial and flexural deformations induced by initial load and the analytical expression for the natural frequency of a simply-supported beam under these effects is derived. A discussion on the analytical expression demonstrates the susceptivity of the two types of effects to the magnitude of initial load, beam stiffness and restraint conditions. Based on the same amount of deformation energy produced, the effects of the two types of initial deformations on static and dynamic responses of straight beams with various boundary conditions are compared quantitatively.3. Based on the theory of finite deformation, the governing differential equations are established for circular-arch beams under the effect of initial load by using energy variation method. The effects of various parameters, including the magnitude of initial load, rise and span of arch beam, inertia moment and inertia radius, on the initial load influence factor are discussed and the corresponding static and dynamic characteristics are obtained.4. Based on nonlinear elastic theory and energy variation principle, a more generalized element stiffness matrix, which incorporates stiffness influences of the flexural as well as axial deformations induced by initial load, is given, with the displacement function being a cubic polynomial. A finite element method for static and dynamic analysis considering the effect of initial load is presented, with corresponding computer programs considering the effect of initial load is presented, with corresponding computer programs produced, which facilitates the analysis of real structures with various conformations, stiffness distribution features, loading and boundary conditions. To illustrate this point, the effects of initial uniformly distributed and concentrated loads on the static and dynamic responses of various beams (simply-supported beam, beam fixed at the two ends, beam fixed at one end and simply-supported at the other end, and cantilever beam) are analyzed respectively.5. For spatial curved and straight beams under the loading combination of compression, flexure, torsion and shear, the governing differential equations and corresponding boundary conditions are established by using energy variation principle, taking into account the effect of initial load. The applicability of the equations is discussed.