Dragan D. Milašinović

Rheological–dynamical analogy: modeling of fatigue behavior

Present paper relates to the analysis of fatigue and fatigue failure of thin long steel bars with the application of a new rheological model and rheological–dynamical analogy (RDA). The analogy has been developed on the basis of mathematical–physical analogy between rheological model and dynamical model with viscous damping, and is aimed to be used for the analysis of inelastic deforming of materials and structures. In this presentation, the aim will be to highlight different aspects of fatigue behavior and fill the gap that other methods cannot. This paper provides a numerical example of obtaining S–N curves of thin long steel bars using RDA model and description of the hysteretic energy dissipation of material subjected to cyclic stresses. First the axial fatigue setup and the experimental results are discussed. The latter in order to demonstrate the ability of the RDA modeling technique, the comparison with Griffith’s theory of fracture is presented. RDA method for fatigue crack growth rate is proposed and compared with Paris power law. On the basis of the comparisons, the present RDA method could be considered as valid and suitable for modeling of fatigue behavior.

Rheological–dynamical analogy: prediction of buckling curves of columns

Abstract This paper is concerned with a new proposal regarding the analysis of inelastic deforming of materials and structures and is based on mathematical–physical analogy between rheological model and dynamical model with viscous damping. Due to the analogy, it becomes obvious that inelastic response of engineering structures is essentially a dynamical problem. The analogy exists for this specific model, and is one out of many examples of the analogies that can be observed in mechanics, as well as between mechanical and electrical (thermal, magnetic, etc.) systems, by virtue of their mathematical descriptions. Generally speaking, the rheological–dynamical analogy (RDA) is derived in order to solve the dynamical problems, but can also be used to explain any statical problems, considering the correspondent limit values of presented mathematical expressions. The paper deals with the buckling problem regarding steel, timber and concrete columns. Using the examples of typical columns, it has been demonstrated that results obtained by RDA are in good accordance with those available in cited references.

MPI-CUDA parallelization of a finite-strip program for geometric nonlinear analysis: A hybrid approach

A finite-strip geometric nonlinear analysis is presented for elastic problems involving folded-plate structures. Compared with the standard finite-element method, its main advantages are in data preparation, program complexity, and execution time. The finite-strip method, which satisfies the von Karman plate equations in the nonlinear elastic range, leads to the coupling of all harmonics. However, coupling of series terms dramatically increases computation time in existing finite-strip sequential programs when a large number of series terms is used. The research reported in this paper combines various parallelization techniques and architectures (computing clusters and graphic processing units) with suitable programming models (MPI and CUDA) to speed up lengthy computations. In addition, a metric expressing the computational weight of input sets is presented. This metric allows computational complexity comparison of different inputs.

Hybrid MPI/OpenMP cloud parallelization of harmonic coupled finite strip method applied on reinforced concrete prismatic shell structure

Application of hybrid parallelization model coupling MPI with OpenMP.Rational usage of cloud computer resources in hybrid parallelization.Analysis of impact of cluster nodes and CPU cores number to parallelization effects.Harmonic coupled finite strip method application on shell structures.Method demonstrated on reinforced concrete prismatic shell structure. This paper discusses the cloud computing based approach for parallelization of large displacement stability analysis of orthotropic prismatic shell structures with simply supported boundary conditions along the diaphragm-supported edges. We review the harmonic coupled finite strip method (HCFSM), and describe a software system for nonlinear analysis of reinforced concrete (RC) structures. We combine different parallelization models - MPI and OpenMP - in order to cope with the increased computational complexity, which originates from coupling of all series terms in the HCFSM formulation. We discuss the effects of parallelization from the perspective of a cloud environment. Our results show that rational usage of cloud resources can lead to significant performance improvements and monetary savings. In certain cases, the achieved performance can be very close to the maximum one.

Rheological‐Dynamical Theory of Visco‐Elasto‐Plasticity and Fatigue: Part 1

This paper is concerned with a new proposal regarding the analysis of visco‐elastoplasticity and fatigue and is based on rheological‐dynamical theory. Due to the analogy between rheological model and dynamical model with viscous damping, it becomes obvious that inelastic response of members is essentially a dynamical problem. An analytical rheological‐dynamical viscoelasto‐ plastic solution of one‐dimensional longitudinal continuous vibration under loading and solution for the stress relaxation as unloading have been developed and used to obtain the fatigue limit of thin long bars. Rheologic behavior of the bar can be characterized by one parameter, like in a single‐degree‐of‐freedom spring mass system. In all inelastic strains time rate effects are always present to some degree. Whether or not their exclusion has a significant influence on the prediction of the material fatigue behavior depends upon several factors like: maximum absolute stress in the cycle, coefficient of asymmetry of cycle, creep coefficient, slope of the strain hardening portion of the stress‐strain curve, relative frequency and uniaxial yield stress. This paper provides description of dynamic magnification factor, relaxation of stress, stress concentration and the fatigue limit of thin long symmetrical bars.

Large displacement stability analysis of thin plate structures: Scope of MPI/OpenMP parallelization in harmonic coupled finite strip analysis

The paper presents large displacement stability analysis of orthotropic thin plate structures with different boundary conditions along the diaphragm-supported edges. A semi-analytical harmonic coupled finite strip method (HCFSM) is used to solve the large deflection and the post-buckling problems or may be applied to both problems simultaneously. The stability of equilibrium states is assessed by looking at the eigenvalues of tangent stiffness matrix of structure. In the HCFSM formulation the coupling of all series terms dramatically increases computation time when a large number of series terms are used. Therefore it is natural to use parallel programming standards, such as MPI and OpenMP to speed up computation. The examples provided justify the proposed improvements in the conventional FSM and are in accordance with the experimental data.

Rheological‐dynamical Analogy: Frequency Dependence of the System Parameters of Internally Damped Bars

An analytical rheological‐dynamical visco‐elastic solution of one‐dimensional longitudinal continuous vibration of bars has been developed and used to evaluate the validity of the classical analytical elastic solutions. As it is well known, the resonance occurs only in the continuous or singledegree‐of‐freedom ideal elastic system when the excitation frequency ωP is equal to the one of the natural frequency of the bar. However, owing to the visco‐elastic nature of materials and frequency dependence of the damping factor it is useful to consider separately the situations arising when the is positive (system is stable) and when it is negative. Negative damping factor means that the complementary solution of the response would not die away (system is unstable because of the factor e). Rheologic behavior of the bar can be characterized by one parameter, i.e. dynamic time of retardation TK D=1/ω, like in a single‐degree‐of‐freedom spring mass system. RDA model has the same phase angle as a simple single‐degree‐of‐freedom spring mass system with damping in the steady state vibration and from that the damping factor is obtained. This paper provides description of the dynamic magnification factor and the transmissibility of several metallic materials using RDA similitude and could be concluded that an ideally effective antivibration mount material should satisfy at least two requirements: first, it should posses a relatively large damping factor; and second, it should possess a damping factor that either remains constant or decreases only slowly with frequency.

Quasi static and dynamic inelastic buckling and failure of folded-plate structures by a full-energy finite strip method

Abstract A study on how a mathematical material modeling approach named rheological-dynamical analogy (RDA) can be used to predict the quasi static and dynamic inelastic buckling and failure of structures is presented in this paper. An analysis of the uniformly compressed folded-plate structures, made of isotropic materials, is carried out. Two sources of non-linearity, one involving geometrical non-linearity due to large deflection, and the other involving material non-linearity due to inelastic behavior, are analyzed by implementing a full-energy finite strip method (FSM). The material non-linearity is analyzed using the RDA. A very basic continuum damage model with one damage parameter is implemented in conjunction with a mathematical material modeling approach in order to address stiffness reduction due to inelastic behavior. According to the analogy, a very complicated material non-linear problem in the inelastic range of strains is solved as a simple linear dynamic one. The orthotropic constitutive relations are derived and modulus iterative method for the solution of nonlinear equations is presented.