Layer-wise Method Research Articles

Extended layerwise method for laminated composite plates with multiple delaminations and transverse cracks

In this paper, the extended layerwise method (XLWM), which was developed for laminated composite beams with multiple delaminations and transverse cracks (Li et al. in Int J Numer Methods Eng 101:407---434, 2015), is extended to laminated composite plates. The strong and weak discontinuous functions along the thickness direction are adopted to simulate multiple delaminations and interlaminar interfaces, respectively, whilst transverse cracks are modeled by the extended finite element method (XFEM). The interaction integral method and maximum circumferential tensile criterion are used to calculate the stress intensity factor (SIF) and crack growth angle, respectively. The XLWM for laminated composite plates can accurately predicts the displacement and stress fields near the crack tips and delamination fronts. The thickness distribution of SIF and thus the crack growth angles in different layers can be obtained. These information cannot be predicted by using other existing shell elements enriched by XFEM. Several numerical examples are studied to demonstrate the capabilities of the XLWM in static response analyses, SIF calculations and crack growth predictions.

Three-dimensional stress analysis of orthotropic curved tubes-part 2: Laminate solution

Abstract The study described in this paper (Part 2) presents a new simple - input method to study thick laminated composite curved tubes subjected to mechanical loadings. First, a displacement approach of Toroidal Elasticity was chosen to obtain the displacement field of single-layer composite curved tubes (Part 1). Then, a layerwise method is employed to develop the most general displacement field of elasticity for arbitrary laminated composite curved tubes. The principle of minimum total potential energy is applied to calculate stresses in thick composite curved tubes under pure bending moment. The accuracy of the proposed method is subsequently verified by comparing the numerical results obtained using the proposed method with finite element method (FEM), experimental data and a solution available in the literature. The results show good correspondence. Also, the proposed method provides advantages in terms of computational time compared to FEM.

Stress analysis of thick orthotropic cantilever tubes under transverse loading

In this work, a new high-order displacement-based method is proposed to investigate stresses and strains in thick arbitrary laminated orthotropic cantilever straight tubes under transverse loading. The most general displacement field of elasticity for an arbitrary thick laminated orthotropic straight tube is developed. A layer-wise method is employed to analytically determine the local displacement functions and stresses under transverse loading. The accuracy of the proposed method is subsequently verified by comparing the theoretical results with experimental data, finite-element method (FEM), and Lekhnitskii solution. The results show good agreement. In addition, high efficiency in terms of computational time is shown when the proposed method is used as compared with FEM. Finally, several numerical examples for stress and strain distributions in various thick cantilever composite straight tubes subjected to transverse loading are discussed.

Modeling of piezoelectric plates with variables separation for static analysis

In this work, the modeling of laminated composite plates with embedded piezoelectric layers is addressed through a variables separation approach. Both the displacement and electric potential fields are approximated as a sum of separated functions of the in-plane coordinates x, y and the transverse coordinate z. This choice yields to a nonlinear problem that can be solved by an iterative process. That consists of solving a 2D and 1D problem successively at each iteration. In the thickness direction, a fourth and second-order expansion in each layer is considered for the displacements and the electric potential, respectively. For the in-plane description, classical eight-node quadrilateral finite element is used. Numerical examples involving several representative laminates are addressed to show the accuracy of the present LayerWise (LW) method. It is shown that it can provide quasi-3D results less costly than classical LW computations. In particular, the estimation of the transverse stresses which is of major importance for damage analysis is very good.

A simple-input method to analyze thick composite tubes under pure bending moment reinforced by carbon nanotubes

In the present work, thick laminated carbon nanotube-reinforced composite straight tubes subjected to pure bending moments are investigated using a new simple-input analytical method. The most general displacement field of elasticity for an arbitrary laminated orthotropic tube is employed to analytically determine stresses under pure bending moments based on a layer-wise method. The accuracy of the proposed method is subsequently verified by comparing the numerical results obtained using the proposed method and finite element method (FEM) with experimental data. The results show good agreement. Also, high efficiency in terms of computational time is achieved when the proposed method is used as compared with FEM. In addition, effects of using nanotubes in laminated composites on stress distributions of orthotropic straight tubes are investigated.

Modeling of composite plates based on Reissner's Mixed Variational Theorem with variables separation

In this work, the modeling of laminated composite plates is performed through a variables separation approach based on a Reissner's Variational Mixed Theorem (RMVT). Both the displacement and transverse stress fields are approximated as a sum of separated functions of the in-plane coordinates x,y and the transverse coordinate z. This choice yields to a non-linear problem that can be solved by an iterative process. That consists of solving a 2D and 1D problem successively at each iteration. In the thickness direction, a fourth-order expansion in each layer is considered. For the in-plane description, classical Finite Element method is used.Numerical examples involving several representative laminates are addressed to show the accuracy of the present LayerWise (LW) method. It is shown that it can provide quasi-3D results less costly than classical LW computations. In particular, the estimation of the transverse stresses which are of major importance for damage analysis is very good.

Extended layerwise method of laminated composite shells

This paper deals with the accurate description of the multiple delaminations and transverse cracks in double-curved laminated composite shells by using the extended finite element method (XFEM) and layerwise theory (LWT), and develops an extended layerwise method (XLWM) which had been applied to the laminated beams in our previous work (Li et al., 2015 [1]). In the displacement assumption of XLWM, the discontinuous function along the thickness direction is adopted to simulate the displacement discontinuous resulted from multiple delaminations. While the transverse cracks are modeled in in-plane displacements discretization by XFEM. The level set method (LSM) is employed in the present method to track the interfaces resulted from the transverse cracks. The interaction integral method and maximum circumferential tensile criterion are used to calculate the stress intensity factor (SIF) and crack growth angle, respectively. In order to ensure the accuracy of Gauss integral when certain nodes are very close to the crack surface as the crack grows, a local remeshing scheme is developed to shift these nodes without scarifying the mesh quality. In the numerical examples, spherical shells, cylindrical shells and plates with/without multiple delaminations and/or transverse crack are considered to the problems of static responses analysis, SIF calculation and transverse crack arbitrary growth.

An extended Layerwise method for composite laminated beams with multiple delaminations and matrix cracks

SummaryFor the delamination and matrix crack prediction of composite laminated structures, the methods based on the damage mechanics and fracture mechanics are most commonly used. However, there are very few methods that can accurately simulate the delaminations together with matrix cracks, although the in‐plane matrix cracks always exist alongside the delaminations under impact loading. In this work, an extended layerwise method is developed to model the composite laminated beam with multiple delaminations and matrix cracks. In the displacement field, the nodes in the thickness direction are located at the middle surface of each single layer, the top surface and the bottom surface of the composite beams. The displacement field contains the linear Lagrange interpolation functions, the one‐dimensional weak discontinuous function and strong discontinuous function. The strong and weak discontinuous function are applied to model the displacement discontinuity induced by delaminations and the strain discontinuity induced by the interface between the layers, respectively. Because the nodes in the thickness direction are located at the middle surface of each single layer, the extended layerwise method can be conveniently employed to deal with the in‐plane matrix cracks combined with the extend FEM. Copyright © 2014 John Wiley & Sons, Ltd.

Buckling analysis of sandwich plate using layerwise theory

Buckling analysis of sandwich plate was investigated using layerwise method. The formulation was based on the first-order shear deformation theory, and the Rayleigh-Ritz method was used for approximating and determining the displacement field. The results obtained from layerwise theory was compared with finite element results and showed good agreement. This study demonstrated that layerwise theory could describe buckling behavior of sandwich plates with high accuracy and represents a more realistic and acceptable description of behavior of the plates with much less computational cost.

The Settlement Computation of Composite Foundation of Different Typed-Pile Based on the Load Test

The three kinds of the typical pile type are selected, which containing flexibility pile (e.g. rammed cement-soil pile is for short RCSP), rigid pile (e.g. cement-flyash-gravel pile is for short CFGP) and loose material pile (e.g. sand-gravel pile is for short SGP). The seven kinds of the composite foundation are designed, which are CFGP, CSP and GP composite foundation, CFG long pile and sand-gravel short pile (for short CFGLP-GSP), CFG long pile and CFG short pile (for short CFGLP-CFGSP), CFG long-short pile and rammed cement-soil short pile (for short CFGLP-RCSP) , and CFG core pile rammed cement-soil loop pile (for short CFGCP-RCSP) combined composite foundation. According to the load-settlement curves to determining the increment deformation modulus of the every load step, the layer-wise summation method to calculate the settlement of composite foundation is given, and the calculation results and the load-settlement curves are consistent.

An Analytic Solution to the Settlement under the Trapezoidal Distribution of the Strip Load of the Soft Soil Foundation

In order to manage and control the settlement along the highway, and meet the needs of the project, it is necessary to study the settlement calculation and prediction methods. Based on the layer-wise summation method, the derivation of the analytic solution of the final settlement can be done through the use of the calculation mode of additional stress and the Integral transform. With an illustrative example, this paper compares the differences of the value of the settlement derived respectively by the specification method and the analytic method. The graphs give an intuitive indication of the performance of the methods, and enable determination of the cubic capacity of settlement of the whole project, laying the foundation for the calculation of the ripped-rock quantity.

Study on Mechanical Property and Displacement of Latticed Soil Nailing Support

Latticed soil nailing support is a new type of revetment structure, which combined lattice support and soil nailing. It effectively improves the global stability of the foundation pit. Currently, the theoretical research about this supporting method is still not consummate. In this paper, on the basis of soil mechanics and code, the stability of latticed soil nailing support are analyzed by the theory of the retaining wall, soil nail and the model of supporting piles. Then calculate the displacement in the limit state by elastic fulcrum method and the instantaneous displacement by layer-wise summation method. The total displacement can be calculated by the combination of the two displacements above, which is between 3.38mm and 15.43mm and close to the measured data. Simulate excavation and supporting process of the pit by finite difference method, analyze the mechanical property and displacement of latticed soil nailing support. Thus the theory of the calculation method to this supporting model is obtained, offering a reference for the similar projects.

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.

Prediction of tensile strength of discontinuous carbon fiber/polypropylene composite with fiber orientation distribution

This study proposes the layer-wise method (LWM) as a new approach for predicting the tensile strength of discontinuous fiber-reinforced composites that have arbitrary fiber orientation angles. The LWM assumes the discontinuous fiber-reinforced composites are identical to laminates that are composed of unidirectional fiber-reinforced plies and have the same distribution of fiber angles over the entire laminate. We applied the LWM to discontinuous carbon fiber polypropylene composites and evaluated the effect of fiber length on tensile strength and fracture mode. Simulated results agreed well with those of experiments. In addition, we proposed a simple analytical model based on micromechanics. This analytical model can correctly evaluate the strength and the fracture mode as effectively as the LWM. We also compared these models with a rule of mixture considering the failure criterion of fiber breakage and examined the limitation of the rule of mixture in predicting composite strength.

Study on a New Foundation Stiffness Calculation Model

This paper combined the feature of Winkler foundation model and base model of limited compressible layer based on the layer-wise summation method, on condition that considering the feature of foundation soil, to derived from a newly foundation stiffness calculation model and to verify it.

The Implementation and Assessment of the Nonlinear Finite Element Method Based on the Chord Modulus in Loess Subgrade

The chord modulus method mostly used in the layer-wise summation method to evaluate the total settlement of subgrade at present. In order to analyze the deformation field, it is necessary that one of key problem should be considered and solved how to use the chord modulus to implement the computation of the finite element method. Firstly, this paper reviews the characteristics of chord modulus theory. Secondly, the solution how the chord modulus is introduced into the finite element method is discussed, and subsequently the corresponding nonlinear finite element codes are developed. The computational results show that the nonlinear finite element method based on the chord modulus should be recommended owing to its potential application that it may consider the deformation field of the whole subgrade.

A Simplified Method for Evaluating Earthquake-Induced Differential Settlements of Buildings on Natural Subsoil

In terms of the physical mechanism and features of the dynamic soil-structure interaction during earthquake excitation, a simplified procedure for evaluating the earthquake-induced differential settlement of buildings on natural subsoil is presented. It takes into account of the irregularity of incident seismic waves and the different distribution of vertical dynamic stresses caused by seismic loading under the two sides of building base. Instead of FEM the simplified method based on the layer-wise summation method is used to calculate the settlement of the subsoil with building presence. The cone model proposed by Meek and Wolf is adopted to calculate the dynamic stress distribution under the building. The residual strain potential model of soil under irregular loading and the modulus-softening model are employed to calculate the permanent deformation of subsoil. The simplified method can consider the combined effect of soil, structure and seismic wave reasonably and describe the developing process of differential settlement. The results of large shaking table tests are consistent with the corresponding calculated results.

Three-dimensional solution of axisymmetric bending of functionally graded circular plates

Abstract Based on three-dimensional theory, this paper investigates the axisymmetric bending of transversely isotropic and functionally graded circular plates subject to arbitrarily transverse loads using the direct displacement method. The material properties can arbitrarily vary along the thickness of the plate. The transverse load is expanded in the Fourier–Bessel series and superposition principle is then used to obtain the total response based on the results of each item of the series. For one item of the series of the load, we assume the distributions of the displacements in the radial direction and therefore only the distributions of the displacements in thickness direction are required to find. If the material properties vary in an exponential law, the exact solutions can be obtained for elastic simple support and rigid slipping support, which are satisfied on the every point of the boundaries. Moreover, the analytical solutions are also presented for simply supported and clamped conditions, which are satisfied using Saint Venant principle. Simultaneously, through the layerwise method a semi-analytical solution is proposed for the case of arbitrary variation of the material properties. Finally the numerical examples are presented to verify the proposed method.

Free-edge effects analysis of angle-ply laminates under transverse loading using layer-wise finite-element method with semi-analytical shear stress calculation

Free-edge stress fields are of an utmost localized nature exhibiting steep stress gradients and they rapidly decay with increasing distance from the laminates’ edges. Layer-wise theory has already been used to analyse the stress field at the free edges of the laminates. In this investigation, the layer-wise theory in finite-element method (FEM) is used to analyse the stress field of the laminates’ free edges. In this study, apart from the conventional FEM in which the stresses are calculated from the constitutive laws, the shear stress components along the thickness are calculated from the equilibrium equations by employing a semi-analytical approach. It is shown that the obtained stresses from the current investigation are very close to those available from the three-dimensional elasticity solution for a square laminate under transversely double sinusoidal pressure distribution. To investigate the free edge influence on shear stress distribution of laminates under transverse loading, the analyses are performed for three angle-ply lay-ups with clustered and alternating sequences. It is shown that the free edge effects of angle-ply laminates with different stacking sequences under transverse pressure loading could be considerably different from laminates with in-plane loading conditions.

Static and dynamic behavior of simply-supported cross-ply laminated piezoelectric cylindrical panels with imperfect bonding

Three-dimensional state-space analysis is developed for a simply-supported, cross-ply piezoelectric laminated cylindrical panel with interlaminar bonding imperfections. To solve the state equation with variable coefficients, a layerwise method is adopted to transform it to an equation with constant coefficients within each sub-layer of sufficiently small thickness. A linear constitutive relationship, which accounts for the electric field, is adopted to model the adhesive bonding whose effect is considered by introducing interfacial transfer matrices. The problems of bending and free vibration are considered with numerical results presented and discussed.