Damijan Markovic, Rainer Niekamp, Adnan Ibrahimbegović, Hermann G. Matthies and Robert L. Taylor
To provide a computational strategy for highly accurate analyses of non‐linear inelastic behaviour for heterogeneous structures in civil and mechanical engineering applications
Abstract
Purpose
To provide a computational strategy for highly accurate analyses of non‐linear inelastic behaviour for heterogeneous structures in civil and mechanical engineering applications
Design/methodology/approach
Adapts recent developments on mathematical formulations of multi‐scale problems to the recently developed component technology based on C++ generic templates programming.
Findings
Provides the understanding how theoretical hypotheses, concerning essentially the multi‐scale interface conditions, affect the computational precision of the strategy.
Practical implications
The present approach allows a very precise modelling of multi‐scale aspects in structural mechanics problems and can play an essential tool in searching for an optimal structural design.
Originality/value
Provides all the ingredients for constructing an efficient multi‐scale computational framework, from the theoretical formulation to the implementation for parallel computing. It is addressed to researchers and engineers analysing composite structures under extreme loading.
Details
Keywords
Adnan Ibrahimbegović, Igor Grešovnik, Damijan Markovič, Sergiy Melnyk and Tomaž Rodič
Proposes a methodology for dealing with the problem of designing a material microstructure the best suitable for a given goal.
Abstract
Purpose
Proposes a methodology for dealing with the problem of designing a material microstructure the best suitable for a given goal.
Design/methodology/approach
The chosen model problem for the design is a two‐phase material, with one phase related to plasticity and another to damage. The design problem is set in terms of shape optimization of the interface between two phases. The solution procedure proposed herein is compatible with the multi‐scale interpretation of the inelastic mechanisms characterizing the chosen two‐phase material and it is thus capable of providing the optimal form of the material microstructure. The original approach based upon a simultaneous/sequential solution procedure for the coupled mechanics‐optimization problem is proposed.
Findings
Several numerical examples show a very satisfying performance of the proposed methodology. The latter can easily be adapted to other choices of design variables.
Originality/value
Confirms that one can thus achieve the optimal design of the nonlinear behavior of a given two‐phase material with respect to the goal specified by a cost function, by computing the optimal form of the shape interface between the phases.
Details
Keywords
Rainer Niekamp, Damijan Markovic, Adnan Ibrahimbegovic, Hermann G. Matthies and Robert L. Taylor
The purpose of this paper is to consider the computational tools for solving a strongly coupled multi‐scale problem in the context of inelastic structural mechanics.
Abstract
Purpose
The purpose of this paper is to consider the computational tools for solving a strongly coupled multi‐scale problem in the context of inelastic structural mechanics.
Design/methodology/approach
In trying to maintain the highest level of generality, the finite element method is employed for representing the microstructure at this fine scale and computing the solution. The main focus of this work is the implementation procedure which crucially relies on a novel software product developed by the first author in terms of component template library (CTL).
Findings
The paper confirms that one can produce very powerful computational tools by software coupling technology described herein, which allows the class of complex problems one can successfully tackle nowadays to be extended significantly.
Originality/value
This paper elaborates upon a new multi‐scale solution strategy suitable for highly non‐linear inelastic problems.
Details
Keywords
Damijan Markovic, Adnan Ibrahimbegovic and K.C. Park
The purpose of this paper is to describe reduced order modelling based on dynamic flexibility approximation and applied to transient analyses.
Abstract
Purpose
The purpose of this paper is to describe reduced order modelling based on dynamic flexibility approximation and applied to transient analyses.
Design/methodology/approach
This work is based on a recently proposed flexibility‐based component modes synthesis (CMS) approach which was shown to be very efficient for solving large eigenvalue problems. The model reduction approach is based on partionning via the localized Lagrange multipliers method, which makes it very appropriate to handle coupled problems.
Findings
In particular, it is demonstrated in this paper how the utilised model reduction method can be applied only to one part of the structure and efficiently coupled to a full finite element model. The performance of the method is investigated on numerical examples of plate and 3D problems.
Originality/value
The proposed flexibility‐based CMS approach can be used as a very efficient tool for complex engineering structures under dynamic load where the mode superposition method applies. The efficiency of the computations is brought about by the model reduction.