Ramón Abascal

Lamb mode conversion at edges. A hybrid boundary element–finite-element solution

Two general and flexible numerical techniques based on the finite-element and boundary element methods developed by the authors in a previous paper are applied to study Lamb wave propagation in multilayered plates and Lamb mode conversion at free edges for frequencies beyond the first cutoff frequency. Both techniques are supported by a meshing criterion which guarantees the accuracy of the results when a condition is fulfilled. A finite-element formulation is directly applicable to study Lamb wave propagation and reflection by simple obstacles such as a flat edge. In order to tackle Lamb wave diffraction problems by defects with more complex geometries, a hybrid boundary element-finite-element formulation is used. This technique provides a major improvement with respect to the only previous boundary element application on Lamb waves: the connecting boundary might be placed as close to the reflector as desired, reducing greatly the requirement on mesh size. Two main application problems on practical metallic plates are studied and compared with reported numerical, theoretical, and experimental results: (1) Lamb wave propagation in degraded titanium diffusion bonds, and (2) Lamb mode conversion at inclined or perpendicular free edges of steel plates for frequencies beyond the first cutoff frequency.

Ultrasonic guided wave scattering in a plate overlap

Guided wave scattering in a plate overlap is investigated by numerical calculations and experimental measurements of transmission and reflection factors from the overlap region. In the numerical study, a hybrid boundary element-finite element method is used to calculate the guided wave scattered field from the overlap region. Transmission and reflection factors are calculated for incident A0 and S0 Lamb and n0 shear horizontal waves, including higher modes generated through mode conversion phenomena. In addition, parametric studies of transmission and reflection factors in this problem are performed numerically over various incident modes, frequencies, and overlap lengths. For verification and comparison with numerical results, experiments were conducted to measure the transmission and reflection factors for incident Lamb and shear horizontal waves in steel plates with two different overlap areas. The experimental results agree well with the numerical calculations. The numerical and experimental results show that it is highly feasible to carry out efficient Lamb wave nondestructive evaluation (NDE) in overlapped plates and in multilayer structures with various lap joints by selecting various modes and tuning frequency.

On fundamental solutions for the boundary integral equations method in static and dynamic elasticity

Abstract A unified formulation for obtaining fundamental solutions in elastostatics and steady state elasto-dynamics is presented. In both cases the solutions for plane, three-dimensional and axisymmetric problems will be shown although the solution, for the axisymmetric dynamic problem does not present a completely explicit form. A study of the behaviour of the dynamic fundamental solutions for low frequencies is presented and their limits for ω→0 are compared with the static solution. The limiting process has particular interest when the Boundary Integral Equation Method is used to solve external domain plane problems.

Using the boundary element method to solve rolling contact problems

A new approach to steady-state rolling, with and without force transmission, based on the boundary element method is presented. The proposed formulation solves the problem in a more general way than semi-analytical methods, with which it shares some approximations. The robustness and accuracy of the proposed method is reflected in the comparative analysis of the results obtained for three different types of rolling problems involving identical, dissimilar and tyred cylinders, respectively.

Dynamics of Foundations

Dynamics of foundations is part of the more general field dynamic soil-structure interaction, which is concerned with the study of structures based on flexible soils and subjected to dynamic actions that may be directly applied to the structure or transmited through the soil.

2D transient dynamic friction contact problems. I. Numerical analysis

A full formulation for the solution of transient dynamic 2D contact problems using the boundary elements method is presented; some applications will be presented in part II of this paper. This formulation is based upon an incremental iterative procedure, the fundamental characteristics of which are: contact conditions that are allowed to vary, several times if necessary, inside each time step; efficient monitoring and control of the results using certain incoherence parameters, proposed in this paper, which allow adequate selection of the variations to be effected for the next iteration; and a load step cycle process with scale factors. Both organization of the equation systems and the scheme followed in their solution are proposed.

Solving 2D rolling problems using the NORM–TANG iteration and mathematical programming

Abstract In this paper, an approach to steady-state rolling, based on the boundary element method and mathematical programming techniques is presented. The algorithm solves the problem by an enchained iteration with the NORM and TANG parts of the problem. These two parts are solved by different methods because of the different nature of the non-linearities inside each one of them. The normal part has a weak non-linearity and can be solved as a linear complementary problem by the Lemke method, but the tangential part, with a stronger non-linearity, needs other methods. This work presents three different ways to solve this part by using mathematical programming techniques, showing their flexibility and reliability by solving various classic problems.

Transmission and Reflection of A0 Mode Lamb Wave in a Plate Overlap

Lamb wave propagation in a plate overlap is investigated. Transmission and reflection coefficients for incident Lamb waves of A0 mode across the overlap region are numerically calculated using a hybrid BE‐FE method. Transmission and reflection coefficients of the Lamb wave across the overlap region are studied as a function of frequency and overlap length. In addition, mode conversion phenomena from the incident waves within the overlap region are also included in the numerical study. A few experiments were also conducted for measurements of transmission and reflection coefficients for incident A0 mode wave in overlap‐shaped steel plates with two different overlap areas. The experimental results are in good agreement with the numerical calculations. The numerical and experimental results can be used to establish guidelines for NDE in overlapped plates and in multilayer structures with various joints by selecting modes and tuning frequency.

2D transient dynamic friction contact problems. II. Applications to soil-structure interaction problems

The numerical techniques described in part I of this paper are applied to the study of dynamic soil-structure interaction problems relating to superficial and embedded foundations subject to forces and rocking moments of an impulsive nature and to seismic waves. The studies undertaken prove the robustness of the algorithm developed and allow the drawing of important conclusions about the behavior of foundations subject to these types of loads, given the presence of surfaces with friction. These techniques also allow description of the changes that usually occur in the distribution of normal and tangential traction under the aforementioned loads.

Lamb wave scattering by defects: A hybrid boundary element-finite element formulation

A hybrid Boundary Element (FE)-Finite Element (BE) Formulation is applied to study Lamb wave scattering by defects in homogeneous isotropic plates. A BE model of the neighborhood of the defect is combined with a semi-analytical FE non-reflecting boundary condition which accurately models the radiation condition in the plate. A meshing criterion guarantees the accuracy of the results. The numerical results satisfy energy flux conservation and reciprocity within a very tight margin. The accuracy of the code is verified by a series of benchmark problems.