Savvas P. Triantafyllou

Hysteretic Finite Elements for the Nonlinear Static and Dynamic Analysis of Structures

A new numerical analysis procedure is presented for the nonlinear analysis of structures. The proposed methodology is developed within the framework of the direct stiffness method and the hysteretic formulation of finite elements. The derived numerical scheme relies on the natural evolution of localized inelastic quantities within the element, that is, the plastic deformation evaluated at properly defined collocation points rather than the evaluation of global and varying state matrices. This is accomplished by considering the additive decomposition of the total strain rate into elastic and plastic parts. Using the principle of virtual work, an equilibrium expression is derived in which the total applied load is equilibrated by an elastic internal force vector and an additional term acting as a nonlinear correction to the elastic component. The evolution of the plastic components is based on a smooth multiaxial hysteretic law that is derived within the framework of classical plasticity. Examples are presented that demonstrate the validity of the proposed method and its computational advantages with respect to existing methods of inelastic analysis.

Small and Large Displacement Dynamic Analysis of Frame Structures Based on Hysteretic Beam Elements

In this work, a beam element is proposed for the nonlinear dynamic analysis of frame structures. The classical Euler-Bernoulli formulation for the elastic beam is extended by implicitly defining new hysteretic degrees of freedom, subjected to evolution equations of the Bouc-Wen type with kinematic hardening. A linear interpolation field is employed for these new degrees of freedom, which are regarded as hysteretic curvatures and hysteretic axial deformations. By means of the principle of virtual work, an elastoplastic hysteretic stiffness relation is derived, which together with the hysteretic evolution equations fully describes the behavior of the element. The elemental stiffness equations are assembled to form a system of linear global equations of motion that also depend on the introduced hysteretic variables. The solution is obtained by simultaneously solving the entire set of governing equations, namely the linear global equations of motion with constant coefficient matrices, and the nonlinear local ...

Bouc-Wen Type Hysteretic Plane Stress Element

In this work, a plane-stress element is proposed for the elastoplastic dynamic analysis of two-dimensional structures exhibiting hysteretic behavior. The constant-strain triangular element formulation for the elastic case is modified by introducing the Bouc-Wen hysteretic model, properly defined in the 2D stress-strain space. Solutions are obtained by simultaneously solving two sets of governing equations, namely the global equilibrium equations and the local constitutive equations, using a predictor-corrector differential equation solver. In following the proposed method, the linearization of the constitutive relations usually performed in step-by-step solution approaches is avoided. The proposed element is capable of modeling cyclic induced phenomena such as stiffness degradation and strength deterioration. Furthermore, the solution method implemented improves the accuracy of the results without increasing the computational cost of the analysis. Examples are presented which demonstrate the efficiency of...

A hysteretic multiscale formulation for validating computational models of heterogeneous structures

A framework for the development of accurate yet computationally efficient numerical models is proposed in this work, within the context of computational model validation. The accelerated computation achieved herein relies on the implementation of a recently derived multiscale finite element formulation, able to alternate between scales of different complexity. In such a scheme, the micro-scale is modeled using a hysteretic finite element formulation. In the micro-level, nonlinearity is captured via a set of additional hysteretic degrees of freedom compactly described by an appropriate hysteric law, which gravely simplifies the dynamic analysis task. The computational efficiency of the scheme is rooted in the interaction between the micro- and a macro-mesh level, defined through suitable interpolation fields that map the finer mesh displacement field to the coarser mesh displacement field. Furthermore, damage-related phenomena that are manifested at the micro-level are accounted for, using a set of additional evolution equations corresponding to the stiffness degradation and strength deterioration of the underlying material. The developed modeling approach is utilized for the purpose of model validation; first, in the context of reliability analysis, and second, within an inverse problem formulation where the identification of constitutive parameters via availability of acceleration response data is sought.

Logarithmic Spin, Logarithmic Rate and Material Frame-Indifferent Generalized Plasticity

In this work we present a new rate type formulation of large deformation generalized plasticity which is based on the consistent use of the logarithmic rate concept. For this purpose, the basic constitutive equations are initially established in a local rotationally neutralized configuration which is defined by the logarithmic spin. These are then rephrased in their spatial form, by employing some standard concepts from the tensor analysis on manifolds. Such an approach, besides being compatible with the notion of (hyper)elasticity, offers three basic advantages, namely:(i) The principle of material frame-indifference is trivially satisfied ; (ii) The structure of the infinitesimal theory remains essentially unaltered ; (iii) The formulation does not preclude anisotropic response. A general integration scheme for the computational implementation of generalized plasticity models which are based on the logarithmic rate is also discussed. The performance of the scheme is tested by two representative numerical examples.

Towards a Multiscale Scheme for Nonlinear Dynamic Analysis of Masonry Structures with Damage

In this work, a three dimensional multiscale formulation is presented for the analysis of masonry structures based on the multiscale finite element formulation. The method is developed within the framework of the Enhanced Multiscale Finite Element Method. Through this approach, two discretization schemes are considered, namely a fine mesh that accounts for the micro-structure and a coarse mesh that encapsulates the former. Through a numerically derived mapping, the fine scale information is propagated to the coarse mesh where the numerical solution of the governing equations is performed. Inelasticity is introduced at the fine mesh by considering a set of internal variables corresponding to the plastic deformation accumulating at the Gauss points of each fine-scale element. These additional quantities evolve according to properly defined smooth evolution equations. The proposed formalism results in a nonlinear dynamic analysis method where the micro-level state matrices need only be evaluated once at the beginning of the analysis procedure. The accuracy and computational efficiency of the proposed scheme is verified through an illustrative example.

RISK ANALYSIS OF COMPOSITE STRUCTURES BY SUBSET ESTIMATION USING THE HYSTERETIC MULTISCALE FINITE ELEMENT METHOD

Composite materials are being implemented in numerous engineering applications including, though not limited to, the aerospace, auto-mobile and wind turbine industries. Advancements in manufacturing processes enable the production of composites whose macroscopically observed properties are elaborately determined at the microscale. Composites are therefore inherently multiscale materials. Consequently, the reliability of structural systems being comprised of composites heavily depends on the micro-mechanical properties of the latter. In this work, a methodology is presented for the evaluation of failure probabilities of composite structures. The hysteretic multiscale finite element method (HMsFEM) is implemented for the modelling of composites while the subset simulation method is used to evaluate the corresponding probabilities of failure. In the HMsFE method, the nonlinear behaviour of the constituents is accurately modelled in the fine scale, while global solution of the structure is performed in a macro-scale thus significantly reducing the computational cost of the reliability analysis procedure.

Numerical and Experimental Investigations of Reinforced Masonry Structures Across Multiple Scales

This review chapter outlines the outcomes of a combined experimental-numerical investigation on the retrofitting of masonry structures by means of polymeric textile reinforcement. Masonry systems comprise a significant portion of cultural heritage structures, particularly within European borders. Several of these systems are faced with progressive ageing effects and are exposed to extreme events, as for instance intense seismicity levels for structures in the center of Italy. As a result, the attention of the engineering community and infrastructure operators has turned to the development, testing, and eventual implementation of effective strengthening and protection solutions. This work overviews such a candidate, identified as a full-coverage reinforcement in the form of a polymeric multi-axial textile. This investigation is motivated by the EU-funded projects Polytect and Polymast, in the context of which this protection solution was developed. This chapter is primarily concerned with the adequate simulation and verification of the retrofitted system, in ways that are computationally affordable yet robust in terms of simulation accuracy. To this end, finite element-based mesoscopic and multiscale representations are overviewed and discussed within the context of characterization, identification and performance assessment.

The scaled boundary finite element method for the efficient modeling of linear elastic fracture

In this work, a study of computational and implementational efficiency is presented, on the treatment of Linear Elastic Fracture Mechanics (LEFM) problems. To this end, the Scaled Boundary Finite Element Method (SBFEM), is compared against the popular eXtended Finite Element Method (XFEM) and the standard FEM approach for efficient calculation of Stress Intensity Factors (SIFs). The aim is to examine SBFEM’s potential for inclusion within a multiscale fracture mechanics framework. The above features will be exploited to solve a series of benchmarks in LEFM comparing XFEM, SBFEM and commercial FEM software to analytical solutions. The extent to which the SBFEM lends itself for inclusion within a multiscale framework will further be assessed.

A THREE DIMENSIONAL MULTISCALE FORMULATION FOR THE NONLINEAR DYNAMIC ANALYSIS OF MASONRY STRUCTURES

In this work, a three dimensional multiscale formulation is presented for the analysis of masonry structures based on the multiscale finite element formulation. The method is develloped within the framework of the Enhanced Multiscale Finite Element Method. Through this approach, two discretization schemes are considered, namely a fine mesh that accounts for the micro-structure and a coarse mesh that encapsulates the former. Through a numerically derived mapping, the fine scale information is propagated to the coarse mesh where the numerical solution of the governing equations is performed. Inelasticity is introduced at the fine mesh by considering a set of internal variables corresponding to the plastic deformation accumulatimg at the Gauss points of each fine-scale element. These additional quantities evolve according to properly defined smooth evolution equations. The proposed formalism results in a nonlinear dynamic analysis method where the micro-level state matrices need only be evaluated once at the beginning of the analysis procedure. The accuracy and computational efficiency of the proposed scheme is verified through an illustrative example.