Giuseppe Davi

A hybrid displacement variational formulation of BEM for elastostatics

Abstract A variational formulation for symmetric positive definite BEM is derived by using a hybrid displacement functional. The functional is expressed in terms of domain and boundary variables, assumed as independent from one another. The resulting equations involve only boundary displacement variables and the approach gives symmetric and positive definite matrices which can be combined with finite elements. The accuracy and efficiency of the method is tested through comparison of some typical results.

A symmetric and positive definite variational BEM for 2-D free vibration analysis

Abstract A general BEM model for structural dynamics is derived by using a symmetric and positive definite variational formulation. The functional employed involves domain displacements and boundary tractions and displacements. These variables are taken to be independent of one another. The boundary variables are expressed in terms of their nodal values while the domain displacement field is approximated by a linear combination of static fundamental solutions. The source point of the latter is located outside the domain. The resolving system is a linear system and for free vibration a classic linear algebraic eigenvalue problem is inferred. The stiffness and mass matrices are symmetric and positive definite and the domain integral, when associated with the inertial term, can be transformed into a boundary integral. Numerical results are presented to prove the efficiency of the method.

Magneto-Electro-Elastic Bimorph Analysis by the Boundary Element Method.

The influence of the magnetic configuration on the behavior of magneto-electro-elastic bimorph beams is analyzed by using a boundary element approach. The problem is formulated by using the generalized displacements and generalized tractions. The boundary integral equation formulation is obtained by extending the reciprocity theorem to magneto-electro-elastic problems; it is numerically implemented by using the boundary element method multidomain technique to address problems involving nonhomogeneous configurations. Results under different magnetic configurations are compared highlighting the characteristic features of magnetopiezoelectric behavior particularly focusing on the link between interlaminar stress and magnetic induction.

Electroelastic Analysis of Piezoelectric Composite Laminates by Boundary Integral Equations

A boundary integral representation for the electroelastic state in piezoelectric composite laminates subjected to axial extension, bending, torsion, shear/bending, and electric loadings is proposed. The governing equations are presented in terms of electromechanical generalized variables by the use of a suitable matrix notation. Thus, the three-dimensional electroelasticity solution for piezoelectric composite laminates is generated from a set of two partially coupled differential equations defined on the cross section of each individual ply within the laminate. These ply equations are linked through the interface conditions, which allow restoration of the model of the laminate as a whole. For this model, the corresponding boundary integral representation and the relative boundary integral equations are deduced, and their features are discussed. The formulation presented lays out the analytical foundation for the development of the multidomain boundary element method to determine numerically the electromechanical response of piezoelectric composite laminates. Numerical results showing the characteristics of the method are given, and the fundamental behavior of piezoelectric composite laminates is pointed out for both mechanical and electrical loads. I. Introduction P IEZOELECTRIC materials generate an electric field when subjected to strain fields and undergo deformation when an electric field is applied. This inherent electromechanical coupling, known as direct and converse piezoelectric effects, is widely exploited in the design of many devices working as transducers, sensors, and actuators. In addition, piezoelectric materials are of primary concern in the field of advanced lightweight structures, where the smart structure technology is now emerging. 1−4 When piezoelectric members are bonded or merged within a structure, it is possible to combine the mechanical properties of the host structure with the additional capabilities to sense deformation and to adapt the structural response accordingly. The first attempt at the application of smart structures with sensing and control capabilities was concerned with the application of piezoelectric patches on the surfaces of beams and plates to induce strain actions on the passive structure or detect its deformation. The development of this approach, together with the improvement of composite material technology, led to the concept of distributed sensing and control, which can be accomplished by the introduction of piezoelectric layers within composite laminates. More recently, the idea of distributed structural control properties has been fully developed by the use of active fiber composites. 5 In these fiber-reinforced composites, the fiber and the matrix have additional functions besides their typical roles. The fiber, which generally exhibits a piezoelectric behavior, not only accomplishes the task of structural reinforcement, but it also has the function of both sensor and actuator. In this kind of smart structure, an active control of the mechanical response is performed on the basis of the intrinsic properties of the structure material. Some of the fundamental problems involved in the mechanical testing, analysis, and design, namely, failure modes and strength and stiffness degradation under static and cyclic fatigue loads, are not tractable without a thorough knowledge of the

Hybrid numerical technique for evaluating wing aerodynamic loading with propeller interference

Abstract A computational investigation of the interference between wings having different aspect ratios and a tractor propeller has been carried out to accurately determine the time-averaged aerodynamic characteristics of the aircraft in terms of the modified wing loads. At first, the aerodynamic interaction has been studied by modeling the wakes both of propeller and wing, in isolated and coupled configurations. The model is based on a hybrid numerical technique, the free wake analysis (FWA) and boundary element method (BEM), applied to the wakes of a propeller and a wing, respectively. The output data has been compared with those available from the experimental procedures. Subsequently, to describe the effects of the two interacting wakes, a three-dimensional BEM approach for an untapered wingspan was applied to evaluate the wing quasisteady loads. The research focused on the wing pressure coefficient distribution related to the altered upstream conditions of the coupled propeller, hence the wing loads and the pitching moment are computed. The results confirm the advantages of the present approach using the FWA and BEM to identify the aerodynamic features of the mutual interference of a wing and a propeller at angle of attack and at a fixed propeller operating condition. Applications of this numerical hybrid scheme to an isolated wing and propeller, in quasisteady flow conditions, as well as to coupled configurations, are shown in the present paper. They demonstrate that accurate results can be obtained with very low computational effort.

Boundary Integral Formulation for Composite Laminates in Torsion

The three-dimensional elastic stress state in a general composite laminate under twisting load is given. The analysis is carried out through an integral equation formulation that is numerically solved by the boundary element method. The integral representation of the elastic behavior is deduced by means of the reciprocity theorem applied to the actual response of each ply and the problems analytical singular fundamental solutions. The interface continuity conditions due to perfect bonding are considered to complete the laminate mathematical model. The method permits the analysis for generally stacked laminates having general shape of the cross section. By virtue of the formulation characteristics, the stress distributions calculated are not affected by a priori assumptions about their nature. Numerical applications are presented, and the results obtained show that the proposed method allows an accurate prediction of the complete elastic response coupled with meaningful computational advantages.

Explicit Kutta condition for unsteady two-dimensional high-order potential boundary element method

An explicit unsteady pressure Kutta condition is discribed that was directly and efficiently implemented in a time domain high-order potential panel method so as to ensure the pressure equality on the upper and lower surfaces at the trailing edge of the airfoil at each time step.

Analytical solution for composite layered beam subjected to uniformly distributed load

ABSTRACT The article presents an analytical theory for multilayered composite beams subjected to transverse uniformly distributed loads. The formulation is based on a layerwise model characterized by third-order approximation of the axial displacements and fourth-order approximation of the transverse displacements. The layerwise kinematical model is rewritten in terms of generalized variables. The beam equilibrium equations, expressed in terms of stress resultant, allow writing the boundary value governing problem. The layerwise fields are obtained by postprocessing steps. The main advantage is to ensure the accuracy level associated to the layerwise formulations preserving the computational efficiency of the equivalent-single-layer theories.

BEM Formulation of the Trailing Edge Condition

This paper deals with a BEM formulation of the trailing edge condition to determine the potential flow field around an airfoil. It is seen the trailing edge condition is not sufficient to give an unique solution. It is necessary to assign a further condition to eliminate the nonuniqueness of the solution. The approach allows to adopt a discretization into superior order elements. Some preliminary applications show the validity of the formulation.

Integral equation approach to composite laminate analysis

Abstract A comprehensive integral equation based approach is presented to determine the elastic response of composite laminates under axial, bending, shear/bending and torsional loadings. The integral equations governing the laminate behavior are directly deduced from the reciprocity theorem for beam‐type structures by employing the fundamental solution of generalized plain strain anisotropic problems. Taking into account the displacement and stress continuity along the interfaces and the external boundary conditions the formulation is numerically solved by the multidomain boundary element method. The resolving system of linear algebraic equations is solved to provide the solution of the problem in terms of displacements and tractions on the boundary of each ply within the laminate. Once this boundary elastic response is determined the displacements and stresses at any point of the laminate can be computed using the appropriate boundary integral representations. The approach, based on a pointwise formulat...