Hysteretic beam element with degrading bouc-wen models

In this work a beam element based on the finite element method, suitable for the inelastic dynamic analysis of structures is presented. The hysteretic beam element proposed by Triantafyllou and Koumousis [1] is extended to account for stiffness degradation, strength deterioration and pinching phenomena. The behavior of the element is governed by the BoucWen model of hysteresis while stiffness and strength degradation are based on Baber and Wen model [2] and pinching on Foliente’s model [3]. The case of non-symmetrical yielding, important for concrete members, is also taken into account. The proposed formulation is based on additional hysteretic degrees of freedom which herein are considered as hysteretic curvatures and hysteretic axial deformations of the crosssections. The elements are assembled using the direct stiffness method to determine the mass and viscous damping matrices, as well as the elastic stiffness and the hysteretic matrix of the structure. The entire set of governing equations of the structure is solved simultaneously. This consists of the linear global equations of motion and the nonlinear local constitutive evolutionary equations for every element. The system is converted into a state space form and the numerical solution is obtained implementing a variable-order solver based on numerical differentiation formulas (NDFs). In this way linearization at the global structural level is avoided facilitating considerably the solution. Furthermore, degradation phenomena are easily controlled through the model parameters at the element level and not in a macroscopic way which requires a computationally demanding bookkeeping mechanism. Numerical results are presented that validate the proposed formulation and verify its computational efficiency as compared to the standard elastoplastic finite element method and existing experimental data

Material point method for deteriorating inelastic structures

The material point method (MPM) is one of the latest developments in particle in cell methods (PIC). The structure is discretized into a number of material points that hold all the state variables of the system [1] such as stress, strain, velocity, displacement etc. These properties are then mapped to a temporary background grid and the governing equations are solved. The momentum conservation equations (together with energy and mass conservation considerations) are solved at the grid nodes. The state variables of the particles are then updated by transferring the solutions from the grid nodes back to the material points. Since the background grid is used only to solve the governing equations at the end of each computational step it can be reset to its undistorted form and thus mesh distortion and element entanglement are avoided. In this work an explicit MPM accounting for elastoplastic material behavior with degradations is proposed. The stress tensor is decomposed into an elastic and a hysteretic – plastic part [5] where the hysteretic part of the stresses evolves according to a Bouc-Wen type hysteretic rule [2]. The inelastic constitutive material law provides a smooth transition from the elastic to the inelastic regime and accounts for the different phases during elastic loading, unloading, yielding and stiffness and strength degradation. Heaviside type functions are introduced that act as switches, incorporate the yield criterion and the terms for stiffness and strength degradation as in the Bouc-Wen model of hysteresis [2]. The resulting constitutive law relates stresses and strains with the use of the tangent modulus of elasticity, which now includes the Heaviside functions and gathers all of the governing inelastic degrading behavior

Distributed Plasticity Analysis of Frame Structures in Rate Form

Distributed plasticity beam column elements are able to efficiently track hysteretic nonlinear behavior of structures under static or dynamic loading. This is accomplished by a refined discretization of the element in control sections along its length, each one being represented by a set of longitudinal fibers. The global response of the element results from a two level integration. In the first the non-linear stress of every fiber is integrated across the cross-sectional area to derive the constitutive relation of the control section and then integration along the element’s length is proved sufficient to yield the current state of the element. This work focuses on the formulation of both displacement and force based beam-column elements where the internal variables that describe the element’s state, namely fiber stresses or strains are expressed in rate form, herein using Bouc-Wen hysteretic models. Both formulations are derived from a unified approach based on the two field Hellinger-Reissner potential which highlights their differences. For simplicity reasons the methodology is applied on plane frame elements based on Euler–Bernoulli kinematics. The main advantage of expressing the evolution of each internal variable through a differential equation offers the ability to solve the entire set simultaneously with the global structure’s equations of motion in state space form. Accurate solutions are derived from proper implementation of an efficient numerical ODE solver

A rigid body spring network model for the simulation of hysteretic behavior of materials

In this work, a discrete numerical approach is presented to model the hysteretic behavior of materials. Rigid Body Spring Network models (RBSN) that were first proposed by Kawai [1] are extended to account for hysteretic elastoplastic behavior. Discretization is based on Voronoi tessellation, as proposed by Bolander [2]. The domain is discretized into convex polygons that will form the discrete rigid bodies of the model. These are connected with three zero length springs in the middle of their common interfaces. The springs are following the smooth hysteretic Bouc-Wen model which efficiently incorporates classical plasticity with no direct reference to the yield surface. Numerical results both for static and dynamic loading are presented that validate the proposed formulation and verify its computational efficiency as compared to the standard elastoplastic finite element method

Smooth plasticity and damage model for the material point method

In the Material Point Method (MPM) the structure is discretized into a set of material points that hold all the state variables of the system [1] such as stress, strain, velocities etc. A background grid is employed and the variables are mapped to the nodes of the grid. The conservation of momentum equations with energy and mass conservation considerations are solved at the grid nodes and the updated state variables are again mapped back to the material points updating their positions and velocities. The background grid is used only to solve the governing equations at the end of each computational step and then it is reset back to its original undeformed configuration. It is used only as a scratchpad for calculations and thus mesh distortion that constitutes a problem in Finite Element simulations is avoided. In this work the explicit formulation of the MPM is employed. According to the strain decomposition rule the strains are uncoupled into an elastic and an inelastic part. The constitutive law follows a Bouc-Wen [2] type formulation for smooth transition from the elastic to the inelastic regime. In the same manner the constitutive equations for elastoplasticity coupled with damage are smoothed according to Lemaitre’s elastoplastic damage theory [3,4]. The above formulation is expressed and incorporated in the tangent modulus of elasticity as Heaviside type functions that control the inelastic behavior and damage. Results are presented that validate and verify the proposed formulation in the context of the Material Point Method

Genetic Algorithms as a Feature Selection Tool in Heart Failure Disease

A great wealth of information is hidden in clinical datasets, which could be analyzed to support decision-making processes or to better diagnose patients. Feature selection is one of the data pre-processing that selects a set of input features by removing unneeded or irrelevant features. Various algorithms have been used in healthcare to solve such problems involving complex medical data. This paper demonstrates how Genetic Algorithms offer a natural way to solve feature selection amongst data sets, where the fittest individual choice of variables is preserved over different generations. In this paper, a Genetic Algorithm is introduced as a feature selection method and shown to be effective in aiding understanding of such data