Finite element analysis of composite structures with smart constrained layer damping

As composite materials have been used for marine structures such as boats, ships, offshore structures, etc., the effect of FSI should be understood.In particular, FSI effect is expected to be significant for polymer composites because the water density is very comparable to the composites' densities.For example, the density of a carbon composite is approximately 50% greater than the water density.Sandwich composites consisting of very low densities of core materials have lower densities than that of water.As a result, the hydrodynamic mass associated with FSI would be very critical to composite structures under water.The growing use of composites in ship masts, superstructures, deck grates, piping, ducting, rudders, propellers, stacks, and various submarine structures requires extensive modeling and testing to help designers, builders and operators better understand composite response [Mouritz, et al., 2001].These materials are subjected to a wide spectrum of loads during manufacturing and service life.Dynamic loadings, in particular, impact type event, represent a serious design concern for use of composite.Composite structures are more susceptible to impact damage than similar metallic structures which are more ductile in nature and can absorb typically large amounts of energy without failure.Furthermore, the damage in composites from impact can go undetected even when the mechanical properties may be drastically reduced from an impact.For these reasons, numerous experimental and analytical studies have been conducted to study the dynamic response of composites subjected to impact loading [Abrate, 1994;Aslan, et al., 2003;Kwon & Wojcik, 1998].According to the review of past works, most of the research effort has been focused on low velocity impact damage, specifically, the damage predictions, and the evaluation and prediction of residual properties of damaged laminates.All of the research completed thus far has focused on damage in composites under impact loading in dry environments to support development of composites in aircraft structures.As far as dynamic response of structures under water is concerned, a great deal amount of analytical and experimental studies have been conducted on the effect of fluid force on the natural frequencies, damping ratios and mode shapes of vibrating structures in contact with fluid.This is commonly known as the Fluid Structure Interaction (FSI) problem.FSI investigations have supported many problems in submarine signaling, offshore oil structure stability, and ship structure vibrations.Through these studies, many numerical and analytical methods have been developed in order to predict the added mass and the www.intechopen.com Advances in Composites Materials -Ecodesign and Analysis 338resulting changes in natural frequency of a structure in contact with fluid.It has been determined and widely proven that the effect of fluid surrounding a structure decreases the natural frequency of a structure due to the increase in total kinetic energy of the vibrating structure and fluid from the addition of kinetic energy of the fluid.This effect can be interpreted as an added mass to the vibrating structure in the analysis of the dynamic response.Essentially as the structure vibrates, its mass is increased by the mass of the vibrating fluid with which it is in contact, consequently decreasing its natural frequency.Studies of fluid structure interaction and the added mass effect, also known as virtual mass effect, hydrodynamic mass, and hydroelastic vibration of structures, started with Lamb [Lamb, 1921] who calculated the first bending mode of a submerged circular plate.In response to a problem of submarine signaling, Lamb investigated the vibrations of a thin elastic circular plate in contact with water.In his investigation he discovered that the natural frequencies for structures in contact with fluid are lower than the frequencies in air, based on the assumption that the modes shapes are virtually the same in water as in a vacuum.The resonant frequency was determined using Rayleigh's method.Lamb's theortical results were verified experimentally [Powell & Roberts, 1923].Much later, more research was conducted for measuing and calculating natural frequencies of free vibartions of beams and plates under water [Lindholm, et al., 1965; Fu & price, 1979;Kwak, 1996].Another branch of FSI studies is underwater explosion.Both experimental and numerical studies have been conducted for metallic structures [

Finite element analysis of composite structures

Constrained layer damping treatments are widely used in mechanical structures to damp acoustic noise and mechanical vibrations. A viscoelastic layer is thereby applied to a structure and covered by a stiff constraining layer. When the structure vibrates in a bending mode, the viscoelastic layer is forced to deform in shear mode. Thus, the vibration energy is dissipated as low grade frictional heat. This paper documents the efficiency of passive constrained layer damping treatments for low frequency vibrations of cylindrical composite specimens made of glass fibre-reinforced plastics. Different cross section geometries with shear webs have been investigated in order to study a beneficial effect on the damping characteristics of the cylinder. The viscoelastic damping layers are placed at different locations within the composite cylinder e.g. circumferential and along the neutral plane to evaluate the location-dependent efficiency of constrained layer damping treatments. The results of the study provide a thorough understanding of constrained layer damping treatments and an improved damping design of the cylindrical composite structure. The highest damping is achieved when placing the damping layer in the neutral plane perpendicular to the bending load. The results are based on free decay tests of the composite structure.

In this paper, we present an optimal low-order accurate piezoelectric solid-shell element formulation to model active composite shell structures that can undergo large deformation and large overall motion. This element has only displacement and electric degrees of freedom (dofs), with no rotational dofs, and an optimal number of enhancing assumed strain (EAS) parameters to pass the patch tests (both membrane and out-of-plane bending). The combination of the present optimal piezoelectric solid-shell element and the optimal solid-shell element previously developed allows for efficient and accurate analyses of large deformable composite multilayer shell structures with piezoelectric layers. To make the 3-D analysis of active composite shells containing discrete piezoelectric sensors and actuators even more efficient, the composite solid-shell element is further developed here. Based on the mixed Fraeijs de Veubeke–Hu–Washizu (FHW) variational principle, the in-plane and out-of-plane bending behaviours are improved via a new and efficient enhancement of the strain tensor. Shear-locking and curvature thickness locking are resolved effectively by using the assumed natural strain (ANS) method. We also present an optimal-control design for vibration suppression of a large deformable structure based on the general finite element approach. The linear-quadratic regulator control scheme with output feedback is used as a control law on the basis of the state space model of the system. Numerical examples involving static analyses and dynamic analyses of active shell structures having a large range of element aspect ratios are presented. Active vibration control of a composite multilayer shell with distributed piezoelectric sensors and actuators is performed to test the present element and the control design procedure. Copyright © 2005 John Wiley & Sons, Ltd.

The effect of progressive damages in composite materials is incorporated into a geometrically nonlinear solid shell element formulation to investigate the dynamic response of composite structures under the blast wave pressure loading. The effect of material damages such as fiber failures, matrix cracking, and fiber-matrix shearing failures on the behavior of composite structures is addressed via reducing their stiffness corresponding to detected failures. Two separate failure criteria are used for unidirectional and woven composites. In addition, the strain-rate effect on the material strength is taken into account. For the dynamic formulation, the trapezoidal rule is chosen for the time integration. Various numerical analyses of composite panels are conducted under the static and dynamic loading conditions to validate the effectiveness of the present formulation. The analysis results clearly exhibit the significant effect of material damages on the structural behavior of the composite panels. Also, the analysis results are in good agreement with the available experimental data.

An efficient computational framework for hailstone impacts on composite plates utilizing a semi-empirical viscoplastic contact law

The classical step-by-step integration method is commonly used for solving structural dynamic responses, but its performance is highly sensitive to the choice of time step. A large time step can significantly reduce accuracy and stability, while a very small time step greatly diminishes computational efficiency. Data-driven modeling and analysis methods are particularly favored for their potential to replace traditional structural analysis methods. However, traditional data-driven machine learning approaches require substantial amounts of training data to predict structural dynamic responses. Moreover, these methods often function as black boxes, lacking physical interpretability, and acquiring the necessary data can be challenging in practice. To address these limitations, this paper employs a physics-informed neural network (PINN) method for structural dynamic response analysis. The PINN approach incorporates the governing equations of structural dynamics into the neural network’s loss function as physical constraints, endowing the model with physical interpretability. The feasibility and effectiveness of this method are demonstrated through case studies on structural dynamic responses under different excitation scenarios. Numerical results show that the PINN method can accurately analyze structural dynamic responses without relying on system response data, a key advantage over traditional data-driven models. Moreover, unlike the classical step-by-step integration method, the PINN approach operates as a spatial domain optimization process and is independent of time step. Given the critical role of hyperparameters in the performance of the PINN model, this paper systematically investigates the influence of various hyperparameter settings on accuracy and efficiency, uncovering patterns of their impact on structural response analysis. Replication code for this paper will be available on GitHub:https://github.com/duke-iem/AIStructDynSolve.

A consistent co-rotational formulation and numerical procedure for the dynamic analysis of planar Timoshenko beam is presented in detail to demonstrate the finite element analysis techniques of co-rotational formulation for nonlinear dynamic analysis of beam structures. The inertia nodal forces and deformation nodal forces are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory by using the d’Alembert principle and the virtual work principle. The nodal coordinates, incremental displacements and rotations, velocities, accelerations and the equations of motion of the system are defined in terms of a fixed global coordinate system, while the total strains in the beam element are measured in element coordinates which are constructed at the current configuration of the beam element. A practical numerical procedure is proposed to determine the current end cross-section coordinates, element coordinates, and element deformations corresponding to an incremental displacement. An incremental-iterative method based on the Newmark direct integration method and the Newton-Raphson method is employed here for the solution of the 284nonlinear dynamic equilibrium equations. Numerical examples are presented to demonstrate the effectiveness of the proposed method and investigate the effect of the shear deformafion on the dynamic response of the beam structures.

The characteristics of composite materials are of high importance to engineering applications; therefore the increasing use as a substitute for conventional materials, especially in the field of aircraft and space industries. It is a known fact that researchers use finite element programs for the design and analysis of composite structures, use of symmetrical conditions especially in complicated structures, in the modeling and analysis phase of the design, to reduce processing time, memory size required, and simplifying complicated calculations, as well as considering the response of composite structures to different loading conditions to be identical to that of metallic structures. Finite element methods are a popular method used to analyze composite laminate structures. The design of laminated composite structures includes phases that do not exist in the design of traditional metallic structures, for instance, the choice of possible material combinations is huge and the mechanical properties of a composite structure, which are anisotropic by nature, are created in the design phase with the choice of the appropriate fiber orientations and stacking sequence. The use of finite element programs (conventional analysis usually applied in the case of orthotropic materials) to analysis composite structures especially those manufactured using angle ply laminate techniques or a combination of cross and angle ply techniques, as well considering the loading response of the composite structure to be identical to that of structures made of traditional materials, has made the use of, and the results obtained by using such analysis techniques and conditions questionable. Hence, the main objective of this paper is to highlight and present the results obtained when analyzing and modeling symmetrical conditions as applied to commercial materials and that applied to composite laminates. A comparison case study is carried out using cross-ply and angle-ply laminates which concluded that, if the composition of laminate structure is pure cross-ply, the FEA is well suited for predicting the mechanical response of composite structure using principle of symmetry condition. On the other hand that is not the case for angle-ply or mixed-ply laminate structure.

Stochastic finite element analysis of composite structures based on material microstructure

Numerical analysis of dynamic responses of laminated glass window subjected to gas explosions

Four methods for global sensitivity analysis are studied with respect to their applicability in the finite element analysis of composite structures: (1) sensitivities based on the variance conditional expectation involving experimental design, (2) Morris' elementary effects method (including recent improvements to effective trajectory selection), (3) Sobol's main and total sensitivity indices, and (4) the root mean square of approximate derivatives at sampled points. The sensitivities of the first ten natural frequencies to the composite material properties as well as to the ply stack are determined. The methods are compared and an assessment of their applicability is made in the case of a fairly large number (d > 25) of uncertain parameters.

PurposeThe safety assessment of engineering structures under repeated variable dynamic loads such as seismic and wind loads can be considered as a dynamic shakedown problem. This paper aims to extend the stress compensation method (SCM) to perform lower bound dynamic shakedown analysis of engineering structures and a double-closed-loop iterative algorithm is proposed to solve the shakedown load.Design/methodology/approachThe construction of the dynamic load vertexes is carried out to represent the loading domain of a structure under both dynamic and quasi-static load. The SCM is extended to perform lower bound dynamic shakedown analysis of engineering structures, which constructs the self-equilibrium stress field by a series of direct iteration computations. The self-equilibrium stress field is not only related to the amplitude of the repeated variable load but also related to its frequency. A novel double-closed-loop iterative algorithm is presented to calculate the dynamic shakedown load multiplier. The inner-loop iteration is to construct the self-equilibrated residual stress field based on the certain shakedown load multiplier. The outer-loop iteration is to update the dynamic shakedown load multiplier. With different combinations of dynamic load vertexes, a dynamic shakedown load domain could be obtained.FindingsThree-dimensional examples are presented to verify the applicability and accuracy of the SCM in dynamic shakedown analysis. The example of cantilever beam under harmonic dynamic load with different frequency shows the validity of the dynamic load vertex construction method. The shakedown domain of the elbow structure varies with the frequency under the dynamic approach. When the frequency is around the resonance frequency of the structure, the area of shakedown domain would be significantly reduced.Research limitations/implicationsIn this study, the dynamical response of structure is treated as perfect elastoplastic. The current analysis does not account for effects such as large deformation, stochastic external load and nonlinear vibration conditions which will inevitably be encountered and affect the load capacity.Originality/valueThis study provides a direct method for the dynamical shakedown analysis of engineering structures under repeated variable dynamic load.

This paper deals with a modeling of the composite timber-concrete ceiling structure. In the analysis of the composite structure, there is the slip using the contact elements and volume finite elements considered. Numerical modeling is complemented by an analytical calculation. This article aims to determine the stiffness of a particular type of glued strip. Totally eight models of the composite timber-concrete structure have been studied.

Dynamic response of structures is a complex process that is not well understood. Seismic design codes allow structural systems of buildings to behave inelastically during strong ground shaking. While hysteretic energy dissipation due to inelastic behaviour is rather well understood, there exist other energy dissipation mechanisms which are not as well understood. Energy dissipation due to mechanisms other than material nonlinearity are often modelled in the form of a single, velocity proportional damping mechanism with an equivalent viscous damping ratio. In seismic design and dynamic analysis of structures, this equivalent viscous damping ratio is generally taken to be constant (e.g. 2% or 5% of the critical) regardless the response is elastic or inelastic. Instead of making such a strong assumption about the viscous damping ratio, which may have large influence on the peak response levels, it is advisable to use an effective viscous damping estimate based on studying the actual response of real structures responding to dynamic loads. Use of such obtained viscous damping will allow extraction of restoring forces from dynamic force estimates. At low strain-rate levels, such as those observed during seismic response, restoring forces match the resistance that develops during quasi-static loading, a method to estimate effective viscous damping and restoring force empirically from dynamic response of a structure is presented. The method considers inelastic response explicitly, i.e. no linearization assumptions are made for the load-deformation behavior of the structure. The presented method is tested on several computational simulation models with various hysteretic behaviors and a preset constant viscous damping ratio to verify that the algorithm 1) estimates a damping ratio close to the value used in the simulations, and accordingly, 2) captures the hysteretic behavior accurately. The method is illustrated using data obtained from reinforced concrete test specimens subjected to design-level base excitations on an earthquake simulator.