# Laboratory of Computational Mechanics - LAMEC

## Summary

LAMEC is the Laboratory of Computational Mechanics of the Civil Engineering Program of COPPE/UFRJ where the fulfilled works deal with the development of numerical models to solve problems of Civil Engineering and correlate areas.

Professors Webe João Mansur and José Claudio de Faria Telles initiated LAMEC research activities in 1976 developing models based on the Boundary Element Method (BEM). Up to the beginning of the nineties, the works developed at LAMEC focused on the development of BEM formulations and algorithms for the potential theory (Laplace and Poisson equations), problems for groundwater flows in permanent (saturated media and with free surface) and transient regimes, the theory of elasticity and plasticity and elastic and acoustic wave propagation problems.

Later, new problems were added to the Boundary Element Method developments, and other numerical methods (finite element method and finite difference method) began to be used in the laboratory routine.

**Boundary elements**

Research in this area deals with the development of new formulations and computational techniques for elastic, poroelastic and acoustic wave propagation, fracture mechanics, elasticity, plasticity, cathodic protection, etc.

• Computational efficiency and new formulations

• Fracture Mechanics

• Dynamic Analysis in the Frequency and Time Domain

• Plasticity

**General Numerical Methods**

Research in this area includes the development and computational implementation of numerical techniques based on the Boundary Element Method, Finite Element Method and Finite Difference Method to solve problems of Engineering and correlate areas.

Numerical Techniques: Parallel Processing in computer clusters, interactive Solvers, implicit and explicit time domain schemes and frequency domain formulations for acoustics, elastodynamics and poroelastodynamics.

• Finite difference and finite element methods for acoustic wave propagation in poroelastic non-homogenous anisotropic media modeling, time schemes, silent boundaries, frequency domain formulations.

• Finite differences procedures for wave propagation modeling in non-homogenous, anisotropic media: standard formulation, inserted mesh, coupling between acoustic elastic and poroelastic media, time and space operators, silent boundaries.

• Finite element method based procedures for elastic, acoustic and poroelastic wave propagation analysis: coupling between different media, finite element performance, and frequency domain formulations.

**APPLIED RESEARCHES **

**GEOACOUSTICS**

Seismic and acoustic wave propagation in the ocean

**Objectives:**

To qualify professionals with solid knowledge in oil industry wave propagation and in other knowledge areas with emphasis in: seismic wave propagation numerical modeling, submarine acoustics and dynamic soil-structure interaction.

This master’s and doctor’s degree program whose emphasis is the propagation of seismic and acoustic waves and signals is directed to engineers, geophysicists, geologists, mathematicians and professionals acting in correlate areas. Student may choose among a vast number of disciplines at COPPE.

**Dynamic Soil–Structure Interaction**

Finite elements and boundary elements are used to develop computational programs for static and dynamic analysis of non-homogenous and anisotropic elastic, plastic, poroelastic, poroelasto-plastic media. Linear and non-linear interaction with structure and fluids is considered.

Silent boundaries are considered to avoid artificial reflections in finite element mesh truncating boundaries.

Formulations in time and frequency domains are considered. This subject basic disciplines are similar to those of seismic modeling.

**Seismic Modeling and Image**

Geological structures capable of retaining oil: post-migration model

Research in this area includes the development of techniques based on BEM, FEM and FDM for oil and civil construction industry applications.

Up to this moment most of worldwide oil industry case studies employ explicit FDM formulations. Developments related to finite difference implicit schemes and to procedures based on BEM and FEM are being considered. Applications seek to model wave propagation in non-homogenous, anisotropic, acoustic, elastic and poroelastic media. Formulations in the frequency domain are also being considered. This research line approximates to the research line in Soil-Structure Interaction and the basic courses are common.

• Acoustic, elastic and poroelastic modeling

• 2D and 3D reverse time migration (RTM)

• Image condition in reverse time migration (RTM)

• Non-conventional seismic survey simulation (ocean bottom cable)

• Seismic survey in irregular topography regions

• Pressure distribution due to air cannon shooting and its interference with marine fauna

• 3D and 4C non-conventional seismic survey simulation

• Tomography applied to civil structures

**Environmental Acoustics**

This subject deals with the development of computer programs based on FE, FD and CE methods for urban and submarine acoustics modeling.

• Urban acoustics: Acoustic barriers including soil absorption, flat panel interaction, case studies in urban environment

• Sound propagation in shallow and deep waters and interference with marine fauna

• Damage and environmental impact numerical modeling

Diversion structure of Serra da Mesa dam - GO

**Objectives:**

• To qualify professionals with general knowledge in numerical modeling of practical problems in Engineering. Special emphasis is given to the boundary element method and its use to solve diverse problems of continuum mechanics.

• Problems of the linear and non-linear, geometric and physical elasticity theory as well as applications to the potential theory in general are included in the scope of this line.

**Fracture mechanics**

Simulation of elliptical crack in a thick-walled cylinder

Applications of the theory of elasticity to Fracture Mechanics generate some of the most difficult problems to be numerically solved with adequate precision. The singular behavior of the stress fields in the vicinity of the tips of a crack, associated to displacement discontinuities through its surface (the so called crack “openings”) are strongly responsible for that fact. The Boundary Element Method (BEM) has shown reliable results on this subject, at a reasonable computational cost; but the existence of two different surfaces, dividing the same spatial position, causes a degeneration in the boundary integral equation that may impose the continuity of displacements in the crack, if the limit is not properly taken, or even a singularity of the equation system matrix, if two different nodal points, one in front of the other are in different surfaces. Thus, BEM can not succeed on these specific applications if special artifices are not implemented to avoid these problems.

Currently, three alternative formulations are being used. The first one is a complement of the sub-region idea, where the crack surfaces appear as interface extensions, on which the conditions of compatibility and equilibrium are not imposed. The second introduces in the boundary, the so-called hypersingular equation, or surface force equation, to replace the classical equation, only when the source point is localized in one of the crack opposite surfaces. Both formulations have in common the need to separate, in elements, the faces of the cracks or gaps, thus making the numerical approximation more difficult, mainly on the first, whose artificial interfaces are also approximated. The third alternative, traditionally very precise but up to this moment not as general as the others, uses Green functions, corresponding to the infinite medium already with downloaded cracks similar to the problem to be solved, in the role of the fundamental solution of the classical integral equation. Considering that the crack fundamental surface forces are null and the usual knowledge of them in the problem to solve, (that is, natural conditions in the crack) a formulation is obtained, where only the classical integral equation appears not being necessary to place source points in the cracks. This greatly contributes to increase the precision of the results, considering the inexistency of separation in elements at the critical regions (crack surfaces) of the problem.

**Thermal fatigue**

Temperature distribution

Thermal stratification in pipes is one of the concerns of a nuclear power station. Temperature differences in a specific place or in different places of the section can lead to stress differences that may cause cracks due to fatigue. Thus, a bi-dimensional transient thermo-elastic analysis of the stratification problem using the Boundary Element Method is important as well as the assessment of the fatigue occurring in pipelines under this phenomenon.

The pipeline for residual heat removal from the primary circuit of Angra 1 Power Station was analyzed because thermal stratification may occur due to temperature differences in the pipe section. The temperature profile in the outer wall of the pipe was supplied by a temperature monitoring system placed on some sections.

Fatigue was assessed at several critical points through stress changes, and the possibility of occurrence of cracks was estimated in order to forecast the need for preventive or corrective maintenance of the components.

**Cathodic Protection**

Electrochemical potential distribution in Ship Platform P-48

Problems due to corrosion are frequent and occur during several activities where economic and mainly human life losses should be avoided. Economic losses include the cost of substituting components that suffered corrosion or even whole equipment substitution according to the intensity of the damage. Indirect losses include accidental or equipment maintenance stops; equipment efficiency reduction, product leakages or contamination due to corroded pipes, hyper dimensioned projects; etc.

If not fought adequately and in the right time, the damage caused by corrosion may be very serious. One of the several methods used to combat corrosion is cathodic protection, which is employed to protect structures that are buried, immersed or in contact with an electrolyte. In this process protection is achieved through the reduction of the electrode potential to the iron thermodynamic immunity domain, that is, through cathodic polarization, usually by impressed current or sacrificial anodes to a potential where corrosion may be considered insignificant.

The principles of cathodic protection are well described in literature; however its use is still a challenge for project engineers. For example, in a complex geometry structure, such as an offshore platform, the polarization potential is not always the same in the whole metallic surface. Some areas remain under protected, thus subject to corrosion, while overprotected areas may suffer material damages due to hydrogen embrittlement. On the other hand, the interface material / media may suffer modification during the structure service life, such as deposit formation that may modify the protection conditions.

One of the procedures to study cathodic protection is to obtain the material polarization curves in its working environment. Those curves show the relationship between electrode potential and current density for a potential range which varies from absolute absence of protection to overprotection, The combination of experimental results with the use of numerical / computational techniques helps to improve the project methodology allowing a more realistic analysis of the protection system performance, updating the project technique according other ground-breaking engineering areas. This updating is important mainly because of offshore industry going to even deeper waters.

Cathodic protection system modeling of offshore structures needs to consider time variable polarization curves and usually, different for each structure region.

Computational techniques allow the analysis of bi-dimensional, axisimetrical, and three-dimensional problems which are mathematically described by Laplace equation and calculate the electrochemical potential and current density distribution on the interface structure / electrolyte.

**ACOUSTICS**

**Submarine acoustics**

The objective of this research project is to develop analytical numerical models in the frequency domain to simulate acoustic wave propagation in shallow waters along irregular surfaces, considering constant speed and the bottom of the sea as a rigid surface. Boundary conditions at the surface and at the bottom are already incorporated in the fundamental solution for constant depths thus avoiding their separation.

**Acoustics in Eolic Parks**

The energetic crisis that our country is currently suffering, due to lack of investments, encouraged the use of alternative energy sources. Eolic energy is an attractive means for electric energy generation through eolic aero generators.

Factors which may limit possible configurations due to the emission of acoustic noises should be considered in the design of eolic farms. The distance to individual dwellings or to residential áreas is determined based on a prediction of the acoustic noise considering the noises generated by all the aero generators of the eolic park.

The objective of the present project is to develop a numerical model, through the boundary element method, of the noise emission of the aero generators of an eolic park.

**Acoustic Barriers**

The noise emission in crowded streets or highways may be harmful for people living near them.

Studies may be fulfilled through Numerical Simulation using the boundary element method to minimize health hazardous effects in human beings.

## Infrastructure

Basically, the equipment park of the Laboratory of Computational Mechanics of COPPE Civil Engineering Program (LAMEC) is composed of approximately 30 PCs and their peripheral devices such as printers, stabilizers, scanners, etc. Besides, there is a cluster of 24 computers. All the computers are linked composing an internal network at LAMEC which is connected to the general UFRJ network.

## Faculty

**PROFESSORS**

Prof. José Claudio de Faria Telles (professor responsável)

Prof. Webe João Mansur

Prof. José Antônio Fontes Santiago

Prof. José Paulo Soares de Azevedo

Prof. Roberto Fernandes de Oliveira

Prof. Luiz Fernando Taborda Garcia

Profª. Simone Luise Delarue Cezar Brasil (professora Associada da Escola de Química)

Prof. Carlos Eduardo Parente Ribeiro (PENO Adjunct professor)

Prof. Eduardo Gomes Dutra do Carmo (PEN Tenured professor)

**PEC RESEARCHERS**

Solange Guimarães

Djalma Manoel Soares Filho