Luis A. Godoy

A viscoplastic approach to model the flow of granular solids

The flow of granular solids within rigid walls is modeled using continuum mechanics. The problem is represented as a viscoplastic flow in which the discontinuity function is taken as in previous works by Gray and Stiles, while the flow rule is modeled by the von-Mises criterion. The resulting model is incompressible and based on non-associated viscoplasticity. The apparent viscosity results in a non-linear function of the second invariant of the symmetric rate of deformation tensor and of the pressure. Friction, cohesion and fluidity of the granular model are taken into account. The constitutive model has been implemented assuming steady-state, in which the granular material flows under a critical state (incompressible behavior). Discretization of the problem has been carried out by finite elements, with direct iteration techniques to solve the non-linear system of equations. The model has been applied to the massive flow of granular material stored in vertical silos and hoppers with axisymmetric or planar shape. Comparisons with experimental tests performed by other authors are presented, together with parametric investigations to identify the main variables affecting the response.

Buckling of short tanks due to hurricanes

Abstract Buckling of thin-walled, short tanks, under severe wind conditions, is investigated using numerical methods. The shells are representative of cylindrical tanks that failed during hurricane Marilyn in the Caribbean islands in 1995, with radius/thickness ratio of 1900 and radius/height ratio of 5. Several models are employed to study instability: bifurcation buckling from a linear fundamental path, nonlinear analysis of imperfect tank, and dynamic response. Wind is modeled using several pressure distributions in the circumferential direction, and the results are compared with those due to axisymmetric pressure. The results show that for the present very thin-walled short tanks, bifurcation buckling produces good estimates of the critical state; however, the structure is imperfection sensitive and this load is reduced in the order of 30–50%.

Interactive Buckling Analysis of Fiber-Reinforced Thin-Walled Columns

An analytical approximate model, leading to a closed form solution, is presented to account for buckling mode interaction in composite I section columns. Three buckling modes are considered in the analysis: a global mode (Euler mode about the weak axis); a primary local mode (rotation of the flanges and bending of the web); and a secondary local mode (bending of the flanges), which are modeled using analytical functions and four degrees of freedom. The fundamental state is shown to be linear and the three critical states for the isolated modes are found to be stable symmetric bifurcations. Mode interaction analysis in terms of the amplitudes of first order fields is carried out, for the first time, for prismatic sections of composite material. The tertiary (coupled) path involves coupling between the two local modes and it describes the sensitivity to imperfections of the buckling behavior of the composite column. A salient feature of the model presented is the closed form of the resulting solution, which enables the designer to easily perform parametric studies. Also, this is the first buckling mode interaction study for thin-walled composite columns. Numerical examples are presented to validate the results and to show the influence of the geometry and properties of the composite on the interaction phenomenon.

Localized support settlements of thin-walled storage tanks

Abstract This paper investigates the influence of support settlements on the out-of-plane displacements of thin-walled cylindrical tanks with a fixed top roof. The shell considered is representative of many steel tanks constructed in Puerto Rico and in the United States, and has a ratio between the diameter and the height of the order of 2.5, with slenderness ratio (radius to thickness) of the order of 1,700. The behavior of the tank is investigated using the finite element computer package ABAQUS by means of a geometrically non-linear algorithm for the analysis and linear elastic material behavior. Results are presented for geometrically linear analysis, geometrically nonlinear analysis and bifurcation buckling analysis. It is shown that the equilibrium path is highly non linear and that the shell displays a plateau for a settlement of the order of half the thickness of the shell. Linear results provide a poor indication of the real displacements in the shell, so that geometric nonlinearity should be included in the analysis for working loads.

Influence of the roof on the natural periods of empty steel tanks

The influence of a fixed roof on the natural periods of vibrations of thin-walled aboveground steel tanks with clamped boundary conditions at the base is studied. Tanks with open-top, self-supported roofs, and roofs supported by rafters are considered, along with different tank aspect ratios. The self-supported roof geometries considered include dome, cone, shallow cone, and flat roofs; whereas the rafters supported roofs geometries study cone, shallow cone, and flat roofs. The effect of the aspect ratio, along with the roof configuration on the natural periods is discussed. It was found that the vibration of empty tanks with a fixed roof is dictated either by cylinder modes or roof modes of vibrations. For self-supported roofs predominant roof modes resulted, whereas for tanks with roofs supported by rafters, cylinder modes dominate the dynamic behavior of the tank. Roof dominant modes had natural periods that remain constant regardless of the aspect ratio considered. Cylinder modes, on the other hand, were characterized by natural periods that showed a linear dependence with the aspect ratio of the tank.

Computational simulation of microstructure evolution during solidification of ductile cast iron

Abstract This paper presents a thermomicrostructural model for the simulation of the solidification process of an eutectic ductile cast iron. The thermal balance is written at a macroscopic level and takes into account both the structural component being cast and its mould. Models of nucleation and growth represent the evolution of the microstructure, and the microsegregation of silicon is also considered. The resulting formulation is solved using a finite element discretisation of the macrodomain, in which the evolution of the microstructure is taken into account at the Gauss integration points. The numerical results are presented in terms of cooling curves and are compared with available experimental values. Furthermore, the sensitivity of the response with respect to changes in the cooling rate and nucleation parameters are investigated. The agreement between experimental and computational values is acceptable in both quantitative and qualitative aspects. Ways to improve the computational model are suggested.

An exact strip method for folded plate structures

Abstract An alternative approach for the analysis of folded plate structures is presented. As in the Finite Strip method, Fourier expansions are used in the axial direction in order to simplify the equations, but then exact solutions are used in the transverse direction. In this way it is not necessary to discretize the structure. Only the displacements at the intersection of the plates hold as degrees of freedom. Convergence is reached by increasing the number of longitudinal modes. A complete formulation of the problem and solution procedure is presented. The base functions, stiffness matrices and load vectors are explicitly given in the appendices. A FORTRAN computer program called FOPS (folded plate structures) was developed. Numerical examples showing the performance of the element are included.

Effect of Pre-stress States on the Impulsive Modes of Vibration of Cylindrical Tank-liquid Systems under Horizontal Motions

In this paper we investigate the influence of hydrostatic pressure and self-weight loads (pre-stress state) on the natural periods and mode shapes of steel cylindrical tanks and on the response under horizontal motions. The tank structure is modeled with finite elements and added mass models are used to represent the liquid. Only the impulsive component of the hydrodynamic response is considered. The natural periods and mode shapes for tank-liquid systems including and neglecting the effect of the pre-stress state are computed and compared. Three tank-liquid systems with different cylinder height to diameter ratios and slenderness ratios are considered. The numerical results show that the pre-stress state has a significant influence in the natural periods and mode shapes of tank-liquid systems with thinner walls; however, for thicker shells this effect is reduced. When the pre-stress state is neglected and included, the smaller differences in natural periods occur, for modes characterized by small circumferential wavenumbers. The steady-state response of a tank-liquid system to horizontal harmonic base accelerations was also computed. Large differences were found when the pre-stress state was neglected. A comparison of the frequency response functions shows that the peak responses occur at quite different load periods and they have significantly different amplitudes.

Imperfection sensitivity of fiber microbuckling in elastic-nonlinear polymer-matrix composites

Abstract Imperfection sensitivity of the fiber micro-buckling problem is a fundamental requirement for applying any fiber micro-buckling model for the prediction of composite compression strength. This paper is devoted to prove theoretically that fiber micro-buckling of elastic-nonlinear polymer-matrix composites is an imperfection sensitive problem. From the proof, it follows that compression strength can be predicted by a suitable model that includes fiber misalignment as the imperfection parameter. The conditions on the behavior of the constituents (fiber and matrix) for imperfection sensitivity are derived. A novel representation for the non-linear shear response of the composite is proposed and supported with experimental data. Also, arguments are presented to support the use of composite constitutive equations rather than using micro-mechanics, particularly when material non-linearity is involved.

Sensitivity of post-critical states to changes in design parameters

Abstract Sensitivity of post-buckling paths is studied in the context of the general theory of elastic stability of discrete structural systems. It is assumed that the sensitivity of the critical state itself has been computed and a formulation is developed to account for sensitivity of the curvature of the post-critical states when there are changes in design parameters. A linear fundamental path is considered. Explicit expressions are obtained for the sensitivities and they take the form of perturbation expansions. Only first order sensitivity of post-critical paths has been developed. A simple example of an angle section column with deformable cross-section illustrates that although a critical state may be insensitive to changes in certain design parameters, the post-critical response may be highly sensitive. In the first example presented (an axially loaded angle section column), the postbuckling response even changes from stable to unstable depending on the values of the design parameter considered.