Alfredo R. de Faria

A Three-Dimensional Ply Failure Model for Composite Structures

A fully 3D failure model to predict damage in composite structures subjected to multiaxial loading is presented in this paper. The formulation incorporates shear nonlinearities effects, irreversible strains, damage and strain rate effects by using a viscoplastic damageable constitutive law. The proposed formulation enables the prediction of failure initiation and failure propagation by combining stress-based, damage mechanics and fracture mechanics approaches within an unified energy based context. An objectivity algorithm has been embedded into the formulation to avoid problems associated with strain localization and mesh dependence. The proposed model has been implemented into ABAQUS/Explicit FE code within brick elements as a userdefined material model. Numerical predictions for standard uniaxial tests at element and coupon levels are presented and discussed.

Modeling of actively damped beams with piezoelectric actuators with finite stiffness bond

The piezoelectric strain actuation of beams has been extensively studied. It is well known that a number of non-idealities may affect the performance of piezoelectric sensors or actuators. In particular, the existence of a finite stiffness bond between the actuator and the structure causes a reduction in the effectiveness (or sensitivity) of induced strain actuators (or sensors) mounted on the surface of a structure. This effect may be significant for short actuators and/or less stiff bonding layers. The objective of this work is to assess the influence of a finite stiffness bond between piezoelectric sensors/actuators and the structure on the active damping of beams subjected to rigid body rotations and elastic deformations. The depoling of the piezoelectric material is also taken into account in the model. A finite element formulation that incorporates this effect is proposed. The formulation uses an Euler-Bernoulli model for the beam and assumes the bond layer to be in a state of pure shear. The effect...The piezoelectric strain actuation of beams has been extensively studied. It is well known that a number of non-idealities may affect the performance of piezoelectric sensors or actuators. In particular, the existence of a finite stiffness bond between the actuator and the structure causes a reduction in the effectiveness (or sensitivity) of induced strain actuators (or sensors) mounted on the surface of a structure. This effect may be significant for short actuators and/or less stiff bonding layers. The objective of this work is to assess the influence of a finite stiffness bond between piezoelectric sensors/actuators and the structure on the active damping of beams subjected to rigid body rotations and elastic deformations. The depoling of the piezoelectric material is also taken into account in the model. A finite element formulation that incorporates this effect is proposed. The formulation uses an Euler-Bernoulli model for the beam and assumes the bond layer to be in a state of pure shear. The effect of the finite bond stiffness appears explicitly in the electro-mechanical coupling matrix. The present formulation includes the effect of the finite bond stiffness with good approximation without introducing extra degrees of freedom in the system. Active damping is introduced in the beam by a simple control law using rate feedback. A numerical example indicates that, within certain limits, the finite stiffness bond may be compensated for by using a higher gain in the control system. However, the finite bonding stiffness has to be taken into account when designing the control system.

Prebuckling Enhancement of Imperfect Composite Plates Using Piezoelectric Actuators

The nonlinear response of initially imperfect composite plates with piezoelectric actuators is investigated. The nonlinearity is limited to the prebuckling regime, where higher order terms present in the strain energy expression can be neglected. The advantage of the electromechanical coupling is exploited in two ways. First, the in-plane piezoelectric stress stiffening effect is used to tailor a stress distribution that inherently increases the critical buckling loads of perfect composite plates by posing an optimization problem that efficiently handles eventual uncertainties involved in the application of mechanical loadings. Second, piezoelectric bending moments are applied in order to avoid or ameliorate the undesirable effects of initial imperfections. An actuation strategy, where the piezoelectric membrane forces and bending moments are decomposed via an appropriate selection of voltages applied to piezoelectric patches that are symmetrically bonded to the top and bottom surfaces of the plate, is proposed and shown to be effective.

Composite-stiffened panel design under shear postbuckling behavior

The metallic airplane structure fuselage design is characterized by skin, frames, stiffeners, and attachments. In most airplanes, the attachments between these components are made by rivets. The influence of the attachments in the panel behavior under diagonal tension can be verified in the metallic Wagner beam. For stiffened composite panels, like metallic Wagner beams, there is insufficient data about attachment design. In order to design and build lightweight composite structures, the analyst must consider different ways in which the skin is connected to the stiffeners and frames. Therefore, the objective of this paper is to investigate different conceptions of a real-reinforced composite panel used in the aeronautical industry. Experimental and numerical results for strains showed good agreement. The finite element model and the criteria used in the failure analysis are also presented. Comparisons between different panel configurations are made, and conclusions are drawn about attachment efficiency.

Thermoelastic analytical solution for 2D composite laminates

Thermo-mechanical phenomena are inherently related to composite materials, from manufacturing to service applications. Therefore, analytical and numerical models developed to simulate composite structural behaviour must satisfactorily account for thermal effects. Pagano’s solutions for 2D and 3D composite problems are usually the base for comparison of the different theories and finite elements developments, even when thermo-mechanical behaviour is assessed. Although a number of papers in the literature use numerical results based on this solution, the formulation accounting for temperature effects is not explicitly presented, nor discussed. The objective of the present paper is to present Pagano’s solution equations for a 2D case of a simply supported beam under a constant temperature field. Results obtained with the derived solution are discussed and compared against a 2D solid Finite Element Model (FEM) generated using a commercial software package.

Critical review of displacement-based laminate theories and modeling techniques

Composite materials present many particularities and challenges when it comes to structural modelling. These challenges come from the anisotropic and nonhomogeneous nature of these materials combined with the continuity requirements of displacement and transverse stresses through the thickness, commonly named Cz requirements. The different approaches developed to assess the structural behaviour of composites can be divided into two major branches: displacement-based theories and mixed-formulation theories. Among the displacement-based theories, the most common approaches are: Equivalent Single Layer (ESLT), that includes the Classical Laminate Theory (CLT); Layerwise Theories (LT), that includes the Zig-Zag Theories (ZZT); Quasi-Layerwise Theories (QLT); and Global-Local Superposition Theories (GLST). The present paper discusses how these different displacement-based models handle the particularities of structural composites, highlighting the main advantages and disadvantages of each formulation, as well as their applicability to common structural problems.

Prediction of Shape Distortions in Composite Wing Structures

Shape distortions and warpage are a major source of problems for composite manufacturers. These distortions are usually accompanied by built up residual stresses. They can deform a component so that it becomes useless. It also has the capability to reduce the strength of the structure. In this paper, the three-dimensional version of the constitutive model originally proposed by Svanberg and Holmberg is employed to predict the warpage of a wing planform. The model takes into account important mechanisms such as thermal expansion, resin shrinkage and frozen-in strains developed during curing cycles. The model was implemented into ABAQUS Finite Element code as a user subroutine UMAT. The macromechanical properties of each composite layer were predicted using a micromechanics based approach, implemented into MATLAB. Results show that wings with cross ply laminates with reducing thickness along the span experienced more warpage than quasi-isotropic laminates. Furthermore, for wings with equal thickness along the span, the results show that the quasi-isotropic laminates experienced more warpage than cross ply laminates. Lastly, the results show that wings with progressively reducing thickness experience twist that is varying from the wing root to the wing tip while wings with a constant thickness experience twist mainly at the centre of the wing

A deep rolling finite element analysis procedure for automotive crankshafts

Deep rolling is performed on crankshafts since the 1960s, yet there is still a knowledge gap regarding residual stress generation. Until this moment, there is no consolidated and widespread procedure to predict such stresses during the crankshaft design cycle. This study establishes an analysis procedure and correlates it with experimental results. An explicit finite element model with real boundary conditions is developed together with a converged mesh for the fillet radius. Simulation nodal displacement and strain output are compared to geometrical measurements using a coordinate-measuring machine. Outputs in terms of residual stresses are related to X-ray diffraction measurements taken along fillet depth. The experimental results attest to the accuracy of the model and correctness in predicting the process outcomes.

A C1 Beam Element Based on Overhauser Interpolation

A NEW C1 ELEMENT IS PROPOSED TO MODEL EULER-BERNOULLI BEAMS IN ONE AND TWO-DIMENSIONAL PROBLEMS. THE PROPOSED FORMULATION ASSURES C1 CONTINUITY REQUIREMENT WITHOUT THE USE OF ROTATIONAL DEGREES OF FREEDOM, USED IN TRADITIONAL ELEMENTS, THROUGH THE USE OF AN OVERHAUSER INTERPOLATION SCHEME FOR BENDING DISPLACEMENTS. THE PRINCIPLE OF VIRTUAL DISPLACEMENTS IS USED TO DETERMINE THE EQUILIBRIUM EQUATIONS AND BOUNDARY CONDITIONS FOR ONE AND TWO-DIMENSIONAL EULER-BERNOULLI BEAMS. THE OVERHAUSER INTERPOLATION IS INTRODUCED AND THE NEW BENDING INTERPOLATION FUNCTIONS ARE DEFINED. FINALLY, BEAM AND FRAME PROBLEMS ARE SOLVED WITH THE NEW FORMULATION AND THE RESULTS ARE COMPARED TO THE TRADITIONAL EULER-BERNOULLI ELEMENT AND EXACT SOLUTIONS.

Robust high-cycle fatigue stress threshold optimization under uncertain loadings

This paper proposes a strategy to achieve robust optimization of structures against high-cycle fatigue when a potentially large number of uncertain load cases are considered. The strategy is heavily based on a convexity property of some of the most commonly used high-cycle design criteria. The convexity property is rigorously proven for the Crossland fatigue criterion. The proof uses a perturbation technique and involves the principal stress components and analytical expressions for the applicable fatigue criteria. The multiplicity of load cases is treated using load ratios which are bounded but are otherwise free to vary within certain limits. The strategy is applied to a notched plate subject to traditional normal and shear loadings that possess uncertain or unspecified components.