Non‐linear dynamic analysis by three‐dimensional ordinary differential equations

Abstract

Purpose

Aims to propose a new dynamic model for the solution of the three‐dimensional structural analysis problem of a non‐linear (non‐symmetrical) structure which is subjected under seismic forces.

Design/methodology/approach

This problem is reduced to the solution of a system of ordinary differential equations of the second kind and such a system is numerically solved by using a special kind of finite elements and by solving the corresponding eigenvalues‐eigenvectors problem.

Findings

The proposed finite element method is much smaller in degree of freedom size than commercial software, as classical linear stiffness matrices of three‐dimensional beam element have six degrees of freedom per node.

Research limitations/implications

Future research should concentrate on the application of the new dynamic model to solve more complicated forms of non‐symmetrical structures.

Practical implications

Practical implications are given to structural analysis problems to the determination of the eigenvalues‐eigenvectors. As an example, an application is given to the determination of the eigenvalues and eigenvectors of a 15‐floor building consisting of reinforced concrete and subjected to an horizontal seismic vibration.

Originality/value

The new dynamic model which is proposed is addressed to researchers of dynamic analysis and civil engineers.

Citation

Ladopoulos, E.G. (2005), "Non‐linear dynamic analysis by three‐dimensional ordinary differential equations", Engineering Computations, Vol. 22 No. 4, pp. 453-479. https://doi.org/10.1108/02644400510598778