Maciej P. Bieniek

Finite element analysis of suspension bridges

Abstract A finite element analysis of static and dynamic response of suspension bridges is presented in this paper. Several finite element models of the three-dimensional bridge structure, with varying degrees of complexity and accuracy, are discussed. The formulation takes into account the geometric nonlinearities of the cables and some elements of the girders-bracingsdeck system as well as the nonlinear material properties of the components. Special attention is given to the effects of steady and unsteady wind forces. Examples of application include calculations of the static and dynamic response of a bridge subjected to wind and moving loads.

A finite difference variational method for bending of plates

Abstract The method of analysis for bending of plates presented in this paper combines a finite difference scheme for the plate strain components and a variational derivation of the equations of motion or equilibrium. The plate strain components are expressed in terms of discrete nodal displacements with the aid of the two dimensional Taylor expansion. Consequently, the virtual work, or the first variation of the strain energy, in an area element is found as a function of the nodal displacements. The derivation of the element forces or the element stiffness matrices and the assembly of the equations of motion or equilibrium follows closely the steps of the finite element method.

An integral equation method for dynamic crack growth problems

Within the assumptions of linear elastic fracture mechanics, dynamic stresses generated by a crack growth event are examined for the case of an infinite body in the state of plane strain subjected to mode I loading.The method of analysis developed in this paper is based on an integral equation in one spatial coordinate and in time. The kernel of this equation, i.e., the influence or Greens function, is the response of an elastic half-space to a concentrated unit impulse acting on its edge. The unknown function is the normal stress distribution in the plane of the crack, while the free term represents the effect of external loading.The solution for the stresses is obtained with the assumption that its spatial distribution contains a square root singularity near the tip of the crack, while its intensity is an unknown function of time. Thus, the orginal integral equation in space and time reduces to Volterras integral equation of the first kind in time. The equation is singular, with the singularity of the kernel being a combined effect of the singularity of the influence function and the singularity of the dynamic stresses at the tip of the crack. Its solution is obtained numerically with the aid of a combination of quadrature and product integration methods. The case of a semi-infinite crack moving with a prescribed velocity is examined in detail.The method can be readily extended to problems involving mode II and mixed mode crack propagation as well as to problems of dynamic external loadings.

Stress-resultant plasticity theories for composite laminated plates

Abstract Constitutive laws are presented for the inelastic analysis of laminated composite plates. The implications of using an elastoplastic theory, applied in a stress-resultant formulation, are discussed and investigated. Two different stress-resultant plasticity theories are proposed, both of which overlook the matrix and fiber inelastic behavior and describe the inelastic response of the laminate as a function of overall laminate properties. Results from numerical experiments with the proposed models are compared with results obtained using a micromechanical elastoplastic composite constitutive model.

CRACK INITIATION AND ARREST UNDER DYNAMIC LOADING

Problems of dynamic fracture have been studied, both theoretically and experimentally, to obtain information about unstable crack extension and arrest. Investigation of bodies containing stationary cracks subjected to rapidly varying applied loads, show: (1) crack initiation; (2) dynamic crack growth; and (3) crack arrest are the dominant features. Experimental observations show that a stationary crack, subjected to a pulse loading, begins to propagate at sometime after the transient loading is applied [1–4]. It is also observed that this elapsed time varies with the magnitude of the pulse loading only [3,4]. Homma et al [5] examined the time history, of the crack-tip, of a semi-infinite Mode I crack under a finite duration pulse load. In this approach, Freund’s fundamental solution [6] was utilized and the crack initiation and arrest times were obtained in closed form. A more complete and detailed analysis of the same approach was given by Freund [7].