General Single Step Single Solve integration algorithm

Direct linear or nonlinear explicit or implicit time integration of structural dynamics problems


Updated 23 Dec 2013

View License

% General Single Step Single Solve (GSSSS) integrator function information:
% -------------------------------------------------------------------------
% function [u,ut,utt,Feff,kiter] = ...
% GSSSS(ExcData,Fint_K_C,m,AlgID,rinf,varargin)
% General linear or nonlinear explicit or implicit direct time
% integration of second order differential equations of SDOF or MDOF
% dynamic systems
% Description
% The General Single Step Single Solve (GSSSS) family of algorithms
% published by X.Zhou & K.K.Tamma (2004) is employed for direct time
% integration of the general linear or nonlinear structural Single
% Degree of Freedom (SDOF) or Multiple Degree of Freedom (MDOF) dynamic
% problem. Selection among 9 algorithms, all designed according to the
% above journal article, can be made in this routive. These algorithms
% encompass the scope of Linear Multi-Step (LMS) methods and are limited
% by the Dahlquist barrier theorem (Dahlquist,1963).
% Input parameters
% ExcData: matrix of two columns, the first column is time and the
% second is the imposed acceleration at the base.
% Fint_K_C: function handle which defines the force - displacement -
% velocity relation of the structure to be analysed. The definition of
% fun must be of the type: [Fint,K,C]=Fint_K_C(u,ut), where Fint is the
% internal force (sum of forces due to stiffness and damping) of the
% structure at displacement u and velocity ut, K and C are the tangent
% stiffness matrix and tangent damping matrix at the same displacement
% and velocity values. Type help Fint_K_C for details.
% m: mass matrix of the structure
% AlgID: ID of the algorithm to be used for the integration. It can be a
% row vector for commonly used algorithms or a suitable string for
% superior optimally designed algorithms. Type help GSSSS for more
% details
% rinf: Minimum absolute value of the eigenvalues of the amplification
% matrix. For the amplification matrix see eq.(61) in Zhou & Tamma
% (2004).
% varargin: optional arguments as follows:
% inflvec: influence vector. It determines the dofs at which the
% acceleration prescribed in ExcData will be imposed (column vector,
% number of Dofs-by-1). Default value 1 for SDOF and ones(DOFs,1)
% for MDOF.
% u0: initial displacement (column vector, number of Dofs-by-1).
% Default value 0 for SDOF and zeros(DOFs,1) for MDOF.
% ut0: initial velocity (column vector, number of Dofs-by-1)
% Default value 0 for SDOF and zeros(DOFs,1) for MDOF.
% maxtol: maximum tolerance of convergence of the Full Newton
% Raphson method for numerical computation of acceleration (scalar).
% Used only for implicit integration. Default value 0.1.
% kmax: maximum number of iterations per increment (scalar). If k=0
% then the integration is explicit and maxtol is not taken into
% account. If k>0 then the integration is implicit. Default value
% 10.
% Output parameters
% u: time-history of displacement
% ut: time-history of velocity
% utt: time-history of acceleration
% Feff: time-history of effective force (due to imposed acceleration,
% relative displacement and relative velocity)
% kiter: iterations per increment
% Copyright (c) 09-Dec-2013
% George Papazafeiropoulos
% First Lieutenant, Infrastructure Engineer, Hellenic Air Force
% Civil Engineer, M.Sc., Ph.D. candidate, NTUA
% Email:
% Website:
% _________________________________________________________________________

Cite As

George Papazafeiropoulos (2023). General Single Step Single Solve integration algorithm (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2012b
Compatible with any release
Platform Compatibility
Windows macOS Linux

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Published Release Notes

Constitutive models were included and documentation for them was provided