Page 251 - Marine Structural Design

Part I1

Ultimate Strength

Chapter 12 A Theory of Nonlinear Finite Element Analysis

12.1 General
A variety of situations exist, in which a structure may be subjected to large dynamic loads,
which can cause permanent deformation or damage to the structure. Therefore, structural
dynamics and impact mechanics have an important role in the engineering design.
Earlier investigations on structural impacts have been well described by Jones (1989). The
development of theoretical methods for impact mechanics has been aided by an idealization of
real complex material behavior as a rigid perfectly plastic material behavior. These methods
are classified as rigid-plastic analysis methods. Theoretical predictions based on rigid-plastic
analyses may give some important information about the impact plastic behavior in a simple
form. The results are often in good agreement with the corresponding experimental results.
However, it is difficult to make a more realistic modeling of the plastic deformations because
they are interspersed with elastic deformation. Plastic flow causes a change in shape and size,
and the plastic regions may disappear and re-appear. The structure may invoke strain
hardening as well as strain-rate hardening when it is yielded due to time dependent loading.
General solutions for arbitrary types of structures subjected to arbitrary impacts can be
obtained by numerical methods such as finite element methods. Considerable progress has
been made in both the theoretical aspects as well as in the development of general purpose
computer programs for dynamic plastic analysis. Unfortunately, there is insufficient
theoretical knowledge on the effect of strain-rate on material properties and on consistent
constitutive modeling of plasticity. Bench mark tests using a number of well known computer
programs require substantial computer speed and capacity and show that only a few programs
can give reliable solutions (Symonds and Yu, 1985). In addition, such programs are not
particularly well-suited and convenient to use for analysis of complex structures. Therefore,
there is a demand for numerical analysis procedures, which can be used to simulate impact
behavior of frame structures with large displacements and strain hardening as well as strain-
rate hardening.
This chapter presents a simple and efficient procedure for large displacement plastic analysis
of beam-column elements. The elastic stifiess matrix is established by combining a linear
stiffness matrix (Przemienicki 1968), a geometrical stiffness matrix (Archer 1965), and a
deformation stifiess matrix (Nedergaard and Pedersen, 1986). Furthermore, the effect of
plastic deformation is taken into account in an efficient and accurate way by the plastic node
method (Ueda and Yao, 1982, Ueda and Fujikubo, 1986, and Fujikubo et al, 1991). In the
plastic node method, the distributed plastic deformation of the element is concentrated to the
nodes using plastic hinge mechanism. The elastic-plastic stiffness matrices of the elements are
derived without requiring numerical integration.