Keywords: dynamic reanalysis, topological modifications, modal analysis, Ritz vectors.

The main purpose of the reanalysis is to perform efficient numerical procedures to evaluate the structural response after modifications of structural components. The object is to evaluate the structural response for successive modifications in the design without solving the set of modified implicit equations so that the computational cost is significantly reduced [1]. The structural modifications may be imposed by external factors (e.g. design alterations for operational reasons, or discrepancies between the predicted and measured properties of the structures) or by designer in order to improve the characteristic of the response (e.g. layout optimisation). In the latter case joints and member could be added or deleted during the design process so that the geometry of the structures could be modified. In this case the most general case of structural modifications are considered, so that the discussion is simultaneously focused on the following changes:

1. Additions or deletion of joints and members that modify the number of degrees of freedom of the structural systems,
2. Modifications in the geometry with a no further change in the number of degrees of freedom,
3. Alterations of dynamic characteristic of structural systems (mass, damping and stiffness).
4. Alterations of load for both modification of original number and positions of joints and for changing in intensity of external excitations.

In the first item the so called reanalysis with topological modification is focused. Several procedures for the static reanalysis of structures subjected to deterministic loads have been proposed in last decades [1]. Kirsch and Liu [2] proposed a static reanalysis method by introducing a modified initial design in the case of layout modification. Baisheng and Wu [3] focused the study in the static reanalysis in the case of simultaneous changes in addition of joint and members, modification of structural geometries and alteration of loading conditions, basing on a partition of the stiffness matrix and on the combined approximations. On the contrary only few papers have been recently focused in the dynamic reanalysis for the evaluation of the approximate eigenproperties of the modified structural system. Segura and Celigüeta [4] dealt with the problem of the dynamic substructure reanalysis evaluating the vibration modes of the modified structure by a perturbation approach. Rayleigh-Ritz analysis has been utilised by Huang et al. [5] for the evaluation of the approximate eigenvalues and eigenvectors of the modified structure taking advantage of the results of the initial modal analysis of the original structure. Chen and Rong [6] by means of Guyan reduction in conjunction with a perturbation technique proposed a method to generate the Ritz basis vectors.

In this paper a new reanalysis method to evaluate the dynamic response of modified structures with or without topological modifications is presented. The method assumes according to the so-called dynamic modification method [7] all the dynamic modification as pseudo-forces and an unconditionally stable step-by-step procedure is described. This technique overcomes the difficulties with the calculation of the eigenproperties of modified structures by evaluating in appropriate form both the transient and loading operators of the numerical procedure. Moreover the modified structural response is evaluated by adding to the unmodified structural response the one evaluated as a consequence of modified structural parameters.

1

Abu Kasim AM, Topping BHV, "Static reanalysis a review". J. Struct. Engng, ASCE, 1987; 113: 1029-45.

2

Kirsch U, Liu S., "Structural reanalysis for general layout modifications", AIAA J., 1997; 35:382-8. doi:10.2514/2.105

3

Wu B., Li Z., "Approximate reanalysis for modifications of structural layout", Engineering Structures 23, 1590�1596, 2001. doi:10.1016/S0141-0296(01)00060-8

4

Segura M.M., Celigüeta J.T., "A new dynamic reanalysis technique based on modal synthesis", Compuer and Structures, 56, 4, 523-527, 1995. doi:10.1016/0045-7949(94)00550-M

5

Huang C., Chen S.H., Liu Z., "Structural modal reanalysis for topological modifications of finite element systems ", Engineering Structures, 22, 304�310, 2000. doi:10.1016/S0141-0296(98)00111-4

6

Chen S.H., Rong F., "A new method of structural modal reanalysis for topological modifications", Finite Elements in Analysis and Design, 38, 1015-1028, 2002. doi:10.1016/S0168-874X(01)00111-1

7

Muscolino, G., "Dynamically Modified Linear Structures: Deterministic and Stochastic Response", J. of Eng. Mech. (ASCE), 122, 1044-1051,1996. doi:10.1061/(ASCE)0733-9399(1996)122:11(1044)

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £125 +P&P)