Layerwise Finite Element Research Articles

Mixed integer multi-objective optimization of composite structures with frequency-dependent interleaved viscoelastic damping layers

The optimal design of composite structures with frequency-dependent interleaved viscoelastic damping layers is addressed in this paper. The design objective of simultaneously maximizing structural modal damping and frequency and minimizing weight is considered. The design problem is formulated as a mixed integer multi-objective optimization problem and solved by evolutionary algorithm. A layerwise finite element model is used. The Pareto-optimal solutions are obtained for two applications. The results show that the approach is quite useful in integrally designing such kind of composite structures. In particular, it is shown that the inserting position and the material type are two important design parameters.

Unified formulation for a family of advanced finite elements for smart multilayered plates

Families of layer-wise and equivalent single-layer advanced finite elements for the analysis of smart multilayered plates are formulated in a unified framework. The proposed modeling strategy reduces the multifield problem to an effective mechanical plate by the condensation of the electromechanical state into the plate kinematics, which is assumed as a variable order expansion along the plate thickness. Carrera Unified Formulation is invoked to derive the elemental stiffness and mass matrices and the mechanical and magneto-electric equivalent forces. The obtained smart plate finite element equations involves kinematical variables only and this extends the tools developed for multilayered composite plates to smart laminates. Results for simply-supported magneto-electro-elastic multilayered square plates are presented to validate the proposed modeling approach and finite elements and to investigate their features.

A layerwise finite element formulation for free vibration analysis of functionally graded sandwich shells

This paper presents a layerwise finite element formulation for dynamic analysis of functionally graded material (FGM) sandwich shell in thermal and non-thermal environments. The layerwise theory used in this work is based on the first-order shear deformation theory (FSDT) for each layer satisfying the displacement continuity at layer interface. Two configurations of FGM sandwich shells are considered, the first with FGM facesheet and homogenous core, and the second having homogenous facesheets and FGM core. Effective material properties of the FGM are estimated according to two micromechanical models, namely, Voigt’s rule of mixture (ROM) and Mori–Tanaka (MT) scheme. For the shells in thermal environment, a nonlinear temperature distribution in thickness direction is considered and the elastic properties are assumed to be temperature dependent. The results obtained from the proposed formulation are validated with those available in the literature. Natural frequencies obtained from Sanders’, Love’s and Donnell’s shell theories for different geometric and boundary conditions are compared to assess the performance of different shell theories for FGM sandwich shells under non-thermal environment. The effects of volume fraction index, core thickness and temperature gradient on natural frequencies of FGM sandwich shells are investigated. The present formulation is simple, accurate and computationally efficient.

Optimal design of viscoelastic damping structures using layerwise finite element analysis and multi-objective genetic algorithm

An optimization method for design of viscoelastic damping structures is presented. The optimal design problem is formulated as a multi-objective constrained optimization problem. A plate finite element based on the layerwise theory is applied to simplify modeling and optimization process. A modified reference point based non-dominated sorting genetic algorithm with parallel computation is used as optimization algorithm. The effectiveness of the approach is verified by numerical applications. It is shown that simultaneous material layout and geometry optimization can be achieved by combining the advantages of the layerwise finite element analysis and multi-objective genetic optimization, and the method is computationally efficient.

A new C0 higher-order layerwise finite element formulation for the analysis of laminated and sandwich plates

In this paper, a new layerwise plate formulation based on a C0 higher-order finite element model is presented for static and free vibration analyses of laminated composite and sandwich plates. The proposed layerwise theory which is developed for a three layered composite plates, assumes higher-order displacement field for middle layer and first-order displacement field for top and bottom layers. Compatibility conditions are imposed at the layer interface to satisfy the interlaminar displacement continuity. An eight-noded isoparametric element is used to model the plate. The accuracy of the proposed formulation is assessed for linear static and free vibration analyses by comparing the authors’ results with available 3D elasticity, finite element and analytical solutions. It has been shown here that the present finite element formulation is much simpler, straightforward and accurate for static and free vibration analyses of laminated composite and sandwich plates.

Coupled higher order and mixed layerwise finite element based static and free vibration analyses of laminated plates

A unique finite element model for static and free vibration analyses of thick and thin composite laminates is presented. The model is a combination of 3D mixed layerwise and equivalent single layer (ESL) theories. The ESL is employed in the global part of domain. On the other hand, a stack of 3D elements are used for estimation of the local parameters. The transverse inter laminar stresses are determined by using 18 noded 3D mixed layerwise element with 6 DOF per node in the local region. This mixed element incorporates the interlaminar stresses as the nodal DOF in addition to displacements for ensuring continuity of the transverse stresses in the thickness direction. Nine noded 2D elements with 12 DOF per node are used in the global domain. A transition has been developed for connection and compatibility of differently modelled sub-domains. Hamilton’s variational principle has been used for the free vibration analysis. Present static and vibration analyses of laminates are in good agreement with the available elasticity and closed form solutions. The presented combined mesh modelling reduces number of elements to map the entire domain as compared to full 3D model. This results in substantial reduction of DOF and improves the computational efficiency.

Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory

Abstract In this work, a layerwise finite element formulation is presented for the first time for dynamic analysis of two types of functionally graded material (FGM) sandwich plates with nonlinear temperature variation along the thickness and the FGM having temperature dependent material properties. Natural frequencies of sandwich plates made of FGM in thermal environment are presented using a layerwise theory. Two configurations of sandwich plate, one with homogenous facesheets and functionally graded core and the second with functionally graded facesheets and homogenous core are considered. The material properties of both types of FGM sandwich plates are varied according to Mori–Tanaka (MT) scheme and the rule of mixture (ROM). The layerwise theory used in this work is based on the assumption of the first order shear deformation theory in each layer and the displacement continuity is satisfied at each layer interface. In the present investigation, it is seen that the natural frequencies converge with lesser number of elements and the results are found to be accurate. Natural frequencies are presented for FGM sandwich plates with different geometric and elastic properties, thermal load and boundary conditions.

Static Analysis of Buried Pipes Using Coupling between Layerwise Finite Element and Boundary Element Method

Static Analysis of Buried Pipes Using Coupling between Layerwise Finite Element and Boundary Element Method

Dynamic Viscoelastic Incremental-Layerwise Finite Element Method for Multilayered Structure Analysis Based on the Relaxation Approach

AbstractThis paper presents an axisymmetric layerwise finite element formulation for dynamic analysis of laminated structures with embedded viscoelastic material whose constitutive behavior is represented by the Prony-generalized Maxwell series. To account the time dependence of the constitutive relations of linear viscoelastic materials, the incremental formulation in the temporal domain is used. Layerwise finite element has been shown to provide an efficient and accurate tool for the simulation of laminated structure. Most of the previous work on numerical simulation of laminated structures has been limited to elastic material behavior. Thus, the current work focuses on layerwise finite element analysis of laminated structures with embedded viscoelastic material. A computer code based on the presented formulation has been developed to provide the numerical results. The present approach is verified by studying its convergence behavior and comparing the numerical results with those obtained using the ABAQUS software. Finally, and as an application of the presented formulation, the effects of load duration on the dynamic structural responses of multilayered pavements are studied.

Effect of Orientation Angle on Acoustic Radiation Mode Amplitudes of Laminated Composite Plates

In this paper, the acoustic radiation mode’s amplitudes of laminated composite plates are studied. The layer wise finite element model is imposed to determine velocity distributions of laminated composite plates. Based on the acoustic radiation mode, the effects of the panel orientation angle on the first three orders acoustic radiation mode’s amplitude of the laminated composite plates are then discussed. A twelve-layer laminated plate was used as an example, and the numerical simulations results show that the effects of the panel orientation angle on the acoustic radiation amplitude of the laminated composite plates are significant.

Coupled efficient layerwise finite element modeling for active vibration control of smart composite and sandwich shallow shells

The active vibration suppression of smart composite and sandwich shallow shells equipped with distributed monolithic piezoelectric and piezo-fiber reinforced composite (PFRC) sensors and actuators is studied using a four-node quadrilateral shallow shell element based on a fully coupled, accurate and efficient layerwise (zigzag) theory. The shell element uses the concept of electric nodes to satisfy the equipotential condition of electroded sensor surfaces without making any approximations or averaging. The effective electromechanical properties of the PFRC laminas are computed using a coupled three-dimensional iso-field micromechanical model. Both classical (constant gain velocity feedback (CGVF)) and optimal (linear quadratic Gaussian (LQG)) control strategies are studied. A truly collocated actuator–sensor arrangement is proposed and shown to remove the instability in CGVF control of shallow shells with conventionally collocated actuators and sensors. The effects of piezoelectric fiber orientation and volume fraction ratio of PFRC, and the radius of curvature and span to thickness ratio of the shell on the control performance, are studied. It is shown that the LQG control not only suppresses the transient vibration under step/impulse excitations, but also eliminates the beating phenomena under harmonic excitation when the forcing frequency is close to the natural frequency of the system.

An investigation on nonlocal continuum damage models for composite laminated panels

The performance of nonlocal approaches based on nonlocal strains, damage driving forces and damage variables is investigated for progressive damage analysis of thick/moderately thick laminated panels under uniform transverse loading using eight-noded isoparametric finite element based on a global higher-order shear deformation theory including zig-zag function and first-order theory. The nonlocal variables are obtained from corresponding local variables using layerwise finite element with quadratic through the thickness variation in each layer. The effect of nonlocal parameter on convergence of failure load, maximum deflection and damage variables with successive mesh refinement is investigated. It is concluded that the convergence improvement based on all the three nonlocal models is almost same and the nonlocal scale parameter in the range of 0.5–3% of plate/panel dimensions yields a good convergence rate.

Quasi-static analysis of multilayered domains with viscoelastic layer using incremental-layerwise finite element method

This paper presents a layerwise finite element formulation for quasi-static analysis of laminated structures with embedded viscoelastic material whose constitutive behavior is represented by the Prony series. To account the time dependence of the constitutive relations of linear viscoelastic materials, the incremental formulation in the temporal domain is used. This approach avoids the use of relaxation functions and mathematical transformations. A computer code based on the presented formulation has been developed to provide the numerical results. The high accuracy of the method is exhibited by comparing the results with existing solutions in the literature and also with those obtained using the ABAQUS software. Finally, and as an application of the presented formulation, the effects of time and load rate on the quasi-static structural response of asphalt concrete (AC) pavements are studied.

The Research of Structural Parameters on Natural Frequency of Laminated Composite Plates

In this paper, natural frequencies of laminated composite plates were studied. The layerwise finite element model is imposed to determine the natural frequencies of laminated composite plates. The effects of panel orientation angle, elastic modulus ratio and width-depth ratio on the natural frequencies of the laminated composite are then discussed. With an example of a sixteen-laying laminated plate, the numerical simulations show that the factor of key structural parameters to the natural frequencies of the laminated composite plate is panel orientation angle and width-depth ratio.

A nonlinear efficient layerwise finite element model for smart piezolaminated composites under strong applied electric field

In this work, we present an electromechanically coupled efficient layerwise finite element model for the static response of piezoelectric laminated composite and sandwich plates, considering the nonlinear behavior of piezoelectric materials under strong electric field. The nonlinear model is developed consistently using a variational principle, considering a rotationally invariant second order nonlinear constitutive relationship, and full electromechanical coupling. In the piezoelectric layer, the electric potential is approximated to have a quadratic variation across the thickness, as observed from exact three dimensional solutions, and the equipotential condition of electroded piezoelectric surfaces is modeled using the novel concept of an electric node. The results predicted by the nonlinear model compare very well with the experimental data available in the literature. The effect of the piezoelectric nonlinearity on the static response and deflection/stress control is studied for piezoelectric bimorph as well as hybrid laminated plates with isotropic, angle-ply composite and sandwich substrates. For high electric fields, the difference between the nonlinear and linear predictions is large, and cannot be neglected. The error in the prediction of the smeared counterpart of the present theory with the same number of primary displacement unknowns is also examined.

Natural Frequencies and Acoustic Radiation Mode Amplitudes of Laminated Composite Plates Based on the Layerwise FEM

In this paper, the natural frequencies and acoustic radiation mode amplitudes of laminated composite plates are studied. The layerwise finite element model is imposed to determine the natural frequencies and velocity distributions of laminated composite plates. The amplitude of the laminated composite plates are then discussed based on the acoustic radiation mode, the effects of the panel orientation angle, the elastic modulus ratio, the widthdepth ratio, and the damping ratio on the first acoustic radiation mode. A sixteen-layer laminated plate was used as an example, and the numerical simulations and experimental results show that the natural frequencies of the laminated composite plate can be analysed accurately using the proposed model. Furthermore, it is found that the effects of the panel orientation angle and width-depth ratio on the acoustic radiation mode amplitude of the laminated composite plates are significant.

Bending analysis of laminated and sandwich plates using a layer-wise stress model

In this paper, the behavior of laminated composites is investigated using several high order or layer-wise finite element calculations. A layer-wise model and its dedicated C0 eight-node finite element have been originally specifically developed for interlaminar stresses analysis in free edge problem [1,2] or recently for bonding study [3]. This model is the core of the present comparisons. It is based on a typical layer-wise description which represents the laminate as a superposition of Reissner plates coupled by interfacial stresses. This element has 5n degrees of freedom per node (n is the layers number) and is able to predict interlaminar stresses. These out-of-plane stresses are deduced directly from constitutive equations without post-processing steps. While previous papers dealt with the accuracy of these interface stresses, in the present paper the accuracy and validity of displacements and stresses are established on classical benchmark bending examples for composites and sandwich plates. The aim is also a better positioning and promoting of this stress approach deriving from the work of Pagano [4], which is not usually studied in this way.

Singular Behavior of Laminated Skew Composite Materials with Cross-Ply Stacking

This study deals with effects depending on skew angles in skewed-laminated composite materials in macroscopic point of view. Based on higher-order approximation of displacements, subparametric layer-wise finite elements are used to analyze skewed-laminated composite systems. The elements have higher-order shape functions derived from the Lobatto shape functions. The modes of the elements are classified into three groups such as vertex, side, and internal modes. The vertex modes have physical meaning, while side and internal modes with respect to the increase of order of the Lobatto shape functions do not have physical meaning but improve accuracy of analysis. Therefore, fixing mesh arrangement of present analysis, the quality of the analysis can be enhanced without re-meshing work. The approach based on p-version of finite element method is implemented with three-dimensional elasticity theory, while shape functions are developed by combination of one- and two-dimensional shape functions, not using three-dimensional shape functions. Using the accurate and practical proposed technique, macroscopic behavior of skewed-laminated composite materials is investigated.

Numerical Analysis on Consolidation Settlement of Soft Soil Foundation for Artificial Island

With the fast development of technology and growth of population, humans began large-scale construction for artificial island. In the field of artificial island research, settlement calculation is pay great attention. According to the geological data surveyed from one artificial island in northern china, using layer-wise summation method and finite element method which based on effective stress theory and Darcy law, the final settlement of the island is calculated. In the meantime, the result of two methods is comparatively analysis.

A finite element model using a unified formulation for the analysis of viscoelastic sandwich laminates

In this paper we present a layerwise finite element model for the analysis of sandwich laminated plates with a viscoelastic core and laminated anisotropic face layers. The stiffness and mass matrices of the element are obtained by Carrera’s Unified Formulation (CUF). The dynamic problem is solved in the frequency domain with viscoelastic frequency-dependent material properties for the core. The dynamic behaviour of the model is compared with solutions found in the literature, including experimental data.