|
|
||
|
|
|
|
From:
Pentti Varpasuo (Department of Civil Engineering, Imatran Voima Oy, Helsinki, Finland), "Incremental analysis of axisymmetric shallow shells with varying strain-displacement relations", Computer Methods in Applied Mechanics and Engineering Vol. 21, 1980, pp 153-169
INTRODUCTION: The most voluminous work on the above problem known to the author is done at the University of California, Berkeley. The problem has been investigated there by Yaghmai [l1], Sharifi [2], Larsen [3] and Nagarajan [4] during the last years of sixties and in the beginning of seventies. Yaghmai and Sharifi evaluated the element geometry and displacement field in local coordinates and were unable to include the rigid body motion in the displacement pattern. By introducing four node, iso-parametric line element, Larsen solved this problem and his element was later used also by Nagarajan. In this paper an iso-parametric formulation for line elements is also used but, instead of the four node element, we use the two-node, eight degree of freedom element first introduced by Irons and Delpack in 1967 [5].
The incremental load application process:
In the general, nonlinear static finite element analysis, involving large deformations and nonlinear constitutive equations, it is necessary to use an incremental. formulation for principles used to derive equilibrium equations. In our case, when linear elastic constitutive equation is assumed and, in general, strains are assumed to be small when compared to unity, but displacements are assumed to be large when compared to the original configuration of the structure, which is feasible stipulating moderately large (compared to the unity) slope angles, the incrementation procedure is not strictly necessary in load application. This is so because our problem is not path dependent as it would he if, for example, elastic-plastic constitutive equations were applied. If one could devise effective enough, always convergent method for solving a system of simultaneous nonlinear, algebraic equations, one might try finite element formulation in a stated case without load incrementation. This is, however, in the current state of development of solving algorithms for nonlinear systems, not possible and so the load incrementation is the safest choice. To clarify the principle of load inorementation, consider the three consecutive positions of a body in a cartesian coordinate system as shown.....
Page 43 / 256