Multiple Cutouts Research Articles

Buckling optimization of variable-stiffness composites with multiple cutouts considering manufacturing constraints

The progress of the automatic fiber placement (AFP) technique makes it viable to fabricate variable-stiffness (VS) composites with curvilinear fiber paths and promotes the rise of the VS composite design. However, traditional representation methods of fiber paths are not flexible for composites with cutouts and are also inconvenient to cooperate with the gradient-based solver. In this study, a parameterized angle variable scheme (PAVS) by the compactly supported radial basis functions (CS-RBFs) is proposed to represent the continuous fiber paths so that manufacturing constraints including minimal turning radius and gap/overlap can be conveniently related to the curl operation and divergence of the fiber angle vector field. A level set representation method of fiber paths is also provided for comparison. Two buckling optimization frameworks of the VS composite considering manufacturing constraints are then proposed based on these two representation methods. Numerical examples of two square plates with cutouts are conducted. Different numbers of support points, support radii, manufacturing constraints, and initial designs are investigated. Results indicate that the proposed PAVS needs few support points and a small support radius. It can also set initial design easily and describe the manufacturing constraints directly and quantitively.

Stability analysis of plates using cut Bogner-Fox-Schmit elements

In this paper, the classical C1-continuous Bogner-Fox-Schmit (BFS) elements are employed to study the buckling behavior of rectangular plates with multiple cutouts. BFS elements are constructed by taking the tensor product of cubic Hermitian polynomials, and thus, arguably constitute one of the simplest approaches to deriving plate/shell elements. The simplicity, however, comes at the cost of requiring regular/structured discretizations, which significantly restricts their use for applications featuring complex geometrical details. To circumvent this shortcoming, a combination of a fictitious domain approach, in particular the finite cell method (FCM), with BFS elements is proposed. Consequently, a typically geometry-conforming discretization is replaced by a structured Cartesian background mesh in conjunction with a more involved numerical integration of the system matrices. This opens the path to analyzing geometrically more complex structures such as plates with one ore more cutouts. Here, the main focus is on the stability (buckling) analysis of such plates. By means of two numerical examples featuring only one circular cutout, it is shown that the critical load can be obtained with high accuracy using the proposed approach. In this context, the attained numerical results are compared with high-fidelity solutions computed using isogeometric analysis (IGA). Moreover, the position of a circular cutout is optimized to maximize the critical buckling load, before the last example demonstrates the applicability of Cut BFS elements to more complex cutout geometries.

Vibration Analysis of a multi core sandwich composite beam with cutouts—A critical investigation

The prime objective of this research work is focused on assessing the dynamic characteristics of a multi core sandwich composite beam with cutouts.The effect of introducing additional cores in sandwich beams is investigated in detail along with various geometric configurations. Also, the impact of placing multiple cutouts with assorted geometric profiles (Circular, Square, Hexagon and Triangular) in a sandwich structure is also addressed in detail. Finite element technique is deployed for numerical analysis and parametric studies. In addition, the influence of reinforcements in the proposed structure is also presented. From the results, it is evident that square cutouts possess the highest damping capability irrespective of geometric position of its placement. Also, it may be concluded that the geometric position of placing cutoutssignificantly influences the magnitude of frequency levels ranging to maximum of 42% hike at lower modes.Moreover, introduction of cutouts leads to reduction in frequency levels for all the cases up to 20%. Furthermore, secondary investigation of multicore reinforced sandwich beams experiences a maximum reduction in frequency of about 15%.

In-Plane Vibration Analysis of Square Plate with Multiple Cutouts

A theoretical solution method for the in-plane vibration characteristics of the plate with cutouts is proposed in this paper. The energy principle in conjunction with the Rayleigh–Ritz solution technique is adopted for the theoretical modeling of the in-plane vibration of the structure. The energy functions for the plate with cutouts are established by subtracting the energies of the cutout domains from the total energies of the whole plate. To ensure continuity over the entire solution domain, the in-plane displacements are composed of two-dimensional standard Fourier series and supplementary functions. The in-plane eigenmodes of the plates with different square cutouts are compared with the results obtained from the finite element method (FEM), with good agreements. The influences of the cutouts on the in-plane vibration characteristics of the plates with cutouts are investigated by varying the number, size, and position of the cutouts.

Effect of Defects Part II: Multiscale Effect of Microvoids, Orientation of Rivet Holes on the Damage Propagation, and Ultimate Failure Strength of Composites

Material properties at the vicinity of the cut-outs in composites are not entirely defect-free. The nteraction of multiple cutouts like rivet holes, the repercussion of their configuration on crack propagation, and ultimate strength were predicted using Peridynamic method and the results are reported in this article. The effect of microscale defects at the vicinity of the cutouts on macroscale damage propagation were shown to have quantifiable manifestation. This study focused on two to four holes in unidirectional composite plates with 0°, 45°, and 90° fiber directions, while the vicinity of a hole was considered degraded. Numerical results were validated using quantitative ultrasonic image correlation (QUIC) and the tensile test. Both the experimental and numerical results confirmed that the strength of the horizontal configuration is higher than the vertical in the plates with two holes. Furthermore, the square configuration was found to be stronger than the diamond configuration with four holes. When the effect of microscale defects was considered, the prediction of ultimate strength was better compared to the experimental results. The predictive model could be reliably used for progressive damage analysis.

High-order free vibration analysis of elastic plates with multiple cutouts

This paper aims to conduct the free vibration analysis of single-layer and laminated composite plates with multiple cutouts based on the scaled boundary finite element method (SBFEM) incorporated with the precise integration method (PIM) and the technique of the degree of freedom transform. It is applicable to a variety of shaped plates containing cordiform, circular and other complicated cutouts. The key equations are formulated built on the two-dimensional model, and the discretization is carried out in terms of only three translational displacement components as the basic unknowns. The high-order spectral elements are applied in the proposed technique to accurately simulate the arc boundaries of cutouts. Characterized by the important semi-analytical feature of the SBFEM, responses of the transverse free vibration are accurately explored. The derivation of governing equations strictly follows the 3D theory of elasticity without introducing any assumptions. The general solution of the SBFEM key equation is in the form of the matrix exponent, which is calculated by the PIM. As a type of highly precise approach, the PIM is introduced to create the global stiffness matrix from the analytical exponential matrix, which can make sure the eigensolutions with enough accuracy. Aided by the methodology of the kinetic energy formula, the global mass matrix of the perforated plate structure is constructed. According to the thin plates, the degree of freedom transform is employed to lower the dimensions of eigenvalue equation and thus improve the computational efficiency. Numerical examples of flexible square and circular plates with various cutouts reveal that excellent agreement is achieved between the natural frequencies predicted by the developed method and those from other methods and exact solutions. Furthermore, the effect of boundary conditions, skew angles, thickness-to-length ratios and sizes of cutouts on distributions of vibration frequencies is discussed.

On-the-fly construction of surrogate constitutive models for concurrent multiscale mechanical analysis through probabilistic machine learning

Concurrent multiscale finite element analysis (FE2) is a powerful approach for high-fidelity modeling of materials for which a suitable macroscopic constitutive model is not available. However, the extreme computational effort associated with computing a nested micromodel at every macroscopic integration point makes FE2 prohibitive for most practical applications. Constructing surrogate models able to efficiently compute the microscopic constitutive response is therefore a promising approach in enabling concurrent multiscale modeling. This work presents a reduction framework for adaptively constructing surrogate models for FE2 based on statistical learning. The nested micromodels are replaced by a machine learning surrogate model based on Gaussian Processes (GP). The need for offline data collection is bypassed by training the GP models online based on data coming from a small set of fully-solved anchor micromodels that undergo the same strain history as their associated macroscopic integration points. The Bayesian formalism inherent to GP models provides a natural tool for online uncertainty estimation through which new observations or inclusion of new anchor micromodels are triggered. The surrogate constitutive manifold is constructed with as few micromechanical evaluations as possible by enhancing the GP models with gradient information and the solution scheme is made robust through a greedy data selection approach embedded within the conventional finite element solution loop for nonlinear analysis. The sensitivity to model parameters is studied with a tapered bar example with plasticity and the framework is further demonstrated with the elastoplastic analysis of a plate with multiple cutouts and with a crack growth example for mixed-mode bending. Although not able to handle non-monotonic strain paths in its current form, the framework is found to be a promising approach in reducing the computational cost of FE2, with significant efficiency gains being obtained without resorting to offline training.

Novel hybrid robust method for uncertain reliability analysis using finite conjugate map

Due to the limitation of measured data, the random and epistemic uncertainties must be simultaneously handled for the reliability analysis of curvilinear aircraft stiffened panels with multiple cutouts. A hybrid iterative conjugate first-order reliability method (CFORM) and adaptive dynamical harmony search (ADHS) optimization are developed for fuzzy reliability analysis (FRA) of stiffened panels. The proposed global level performs fuzzy analysis using ADHS, while the local level is utilized for reliability evaluation using efficient FORM. In ADHS, two adjusting procedures are implemented to update the new positions of reliability index bounds with dynamical parameters Due to the computational burden of fuzzy reliability analysis with robust iterative formula, a conjugate FORM is applied using finite-step size, which is formulated by applying the Armijo rule. A limited conjugate scalar factor is utilized to determine the conjugate nonlinear describe map. The proposed conjugate formula is examined by various FORM formulas. The fuzzy reliability index is obtained using alpha level set-based ADHS in terms of extracted results by conjugate FORM for stiffened panels. Furthermore, by the sensitivity measure of the fuzzy reliability index, boundaries of uncertainty interval for stiffener heights and thicknesses of the panel were proposed. Moreover, the influences of different stiffener height, design load, stiffener thickness, and skin thickness on buckling mode were discussed. Survey results demonstrated that the proposed FRA is more accurate to handle epistemic uncertainties of curvilinear aircraft stiffened panels than the classic reliability method-based FORM. The conjugate reliability method provides robust and efficient results compared to the modified iterative reliability methods.

Experimental and numerical analysis on vibration of plate with multiple cutouts based on primitive cell plate with double cutouts

An efficient analytical solution is presented in this paper to model the bending vibration of plates with any numbers of cutouts and under arbitrary boundary conditions. Especially we study the efficiency of the model while explore the influence of increasing number of cutouts and increasing area of cutouts on the eigenpairs of the plate. In the first step, the model of the plate with cutouts is decomposed into certain amount of primitive cells with double cutouts and solved based on the Chebyshev-Lagrangian method. The two advantages of this modeling method lie in offering a flexible assemble strategy of primitive cell plates to form plate in various shapes and with arbitrary numbers of cutouts while bringing substantial convenience in calculation owing to the uniformly expanded double Chebyshev series terms for the displacement of each primitive cell plate. Secondly, the experimental and numerical validations are performed and consequent efficiency and convergence analysis is discussed. The results show that the current model presents potential robust in computation efficiency. At last, the influence of several key parameters on eigenpairs of plate with cutouts is investigated, including the boundary restraint of the plate, the number of cutouts and the size of cutouts.

Postbuckling analysis of multi-directional perforated FGM plates using NURBS-based IGA and FCM

Geometric modeling and numerical analysis of multi-directional FGM (Functionally Graded Material) plate, whose material properties grade continuously both in its thickness and in-plane directions, are increasingly required. In this work, postbuckling behavior of this type of plates with multiple cutouts is, for the first time, numerically investigated through the combination of NURBS-based IGA (IsoGeonetric Analysis) and FCM (Finite Cell Method). The nonlinear deformation of plate is determined by TSDT (Third-order Shear Deformation Theory) and von Kármán nonlinear assumptions without the requirement of SCFs (shear correction factors). Besides, the higher continuity advantage of NURBS basis functions can easily meet the C1-continuous requirement of the displacement field. The main contribution is introducing the FCM to deal with the influence of complex cutouts on the postbuckling characteristics. The geometric interfaces of the cutouts are approached and approximated by adaptive quadrature procedure in the distinguished cut elements. The advantage of this implementation is that the previously tricky process of representing the geometry of perforated plate with multiple NURBS patches can be eliminated, which naturally avoids the imposition of C1-continuity condition across the patch boundaries. The cylinder arc-length method combined with modified Newton–Raphson iteration algorithm, which takes into account of the initial geometric imperfections, is applied to implement geometrically nonlinear stability analysis and track the postbuckling paths. The effectiveness and reliability of the presented method are verified with available solutions of isotropic and conventional perfect FGM plates. Subsequently, a series of factors, including material volume fraction, length-to-thickness ratio, boundary condition, cutout size, etc., affecting the postbuckling responses of multi-directional perforated FGM plates are considered and investigated.

A multi-fidelity competitive sampling method for surrogate-based stacking sequence optimization of composite shells with multiple cutouts

In order to explore the global optimizing ability of the surrogate-based stacking sequence optimization of composite shells with multiple cutouts, a multi-fidelity competitive sampling (MFCS) method is developed in this paper, which is composed of a low-fidelity sampling level and a high-fidelity sampling level. In the low-fidelity sampling level, competitive sampling points are determined by means of the prior screening criterion and the further screening criterion in sequence. Based on the POD-based buckling method, a novel reduced-order model is established as the low-fidelity model for fast linear buckling analysis of composite shells with multiple cutouts. In the high-fidelity sampling level, the explicit dynamic method is employed to calculate the post-buckling response of competitive sampling points. Based on these sampling results, a surrogate model is built. Next, a surrogate-based stacking sequence optimization framework is established for minimum material cost of composite shells with multiple cutouts. A simple optimization example of Mishra's Bird test function is performed and the effectiveness of the MFCS method is demonstrated. Finally, the proposed method is used for the surrogate-based stacking sequence optimization of composite shells with multiple cutouts. The optimal result of total material cost by the MFCS method decreases by 23.0% than the optimal result by the traditional sampling method, which indicates that the MFCS method contributes to improving the global optimizing ability of the surrogate-based stacking sequence optimization of composite shells with multiple cutouts.

Effect of multiple cutouts on shear buckling of laminated composite spherical shells

Abstract The shear buckling analysis of laminated spherical shells with multiple cutouts is studied using the present mathematical model. In the present mathematical model, a transverse shear stresses have been varied parabolically across the thickness. The zero transverse shear stress conditions are introduced at the top and bottom of the shell without using a shear correction factor. Further, the cross curvature effect in spherical shells is included via strain relations. In this proposed mathematical model, the unknown parameters are required only at the reference plane. In this paper, a C0 continuity nine noded curved isoparametric element has been considered. Based on the proposed mathematical model, a computer code has been written to find out many new results for the variation in cutouts, boundary conditions, curvature and lamination schemes etc

Response of composite laminate with various cut-out combinations to tension load

All parts like adaptor plates, swash plates, repair patches and components providing way to wires have multiple cut-outs and as composites are replacing metals and alloys in many of these components it is necessary to understand the composite material’s reaction to mechanical loads in presence of cut-outs. In this work, experiments were conducted to note the impact of combination of various cut-outs on the UTS (ultimate tensile strength) of GFRC. Result shows that specimens containing combination of square and circular cut-outs can carry highest loads before failure as compared to other combinations.

Isogeometric analysis and design of variable-stiffness aircraft panels with multiple cutouts by level set method

For composite panels with cutouts, curvilinear fiber path can adjust the in-plane stiffness distribution to increase the buckling resistance, but it results in huge computational cost for the buckling analysis when FEA is employed. In this study, variable-stiffness panels with cutouts are analyzed via isogeometric method, where cutouts are represented by the level set method. The method for suppressing artificial buckling modes is proposed to improve the prediction accuracy. Moreover, the analytical sensitivity is derived to facilitate fiber path optimization, and a new bi-level optimization framework considering manufacturing constraints is established. Finally, the proposed method is verified by variable-stiffness aircraft panel with multiple cutouts, which can not only provide an accurate prediction of buckling load, but also exhibit high convergence rate and low computational cost for fiber path optimization.

Dynamic Analysis of Laminated Composite Rhombic Elliptic Paraboloid due to Mass Variation

AbstractThe present paper is the first study of free vibration analysis of laminated composite rhombic (skew) elliptic paraboloids with mass variation via multiple cutouts and concentrated mass. To...

Study on the Stress Concentration in GFRP Composite Plates with Multiple Cut-Outs Subjected to Shear Loading

The composite materials are widely used nowadays as major parts of structures in many industries like aerospace, marine, automobile, space vehicles and also for the repair and replacement of civil infrastructures. Stresses are vital parameters considered in the design of structures. Any irregularities in shape, materials, or the presence of cut-outs create localized stress concentration and reduce the capacity of the material to take loads. The anisotropic behaviour of composite structures also makes the analysis more complex. Shear loading often exists in the engineering practices such as in aerospace due to heavy aerodynamic loads. So in the present study the effects of different parameters like layup sequences, number of plies, proximity of cut-outs, shapes and arrangements of cut-outs under in-plane shear loading on the glass fibre reinforced polymer (GFRP) plate with multiple cut-outs are studied using ABAQUS. The results from the study show that all the parameters considered for the study affects the stress concentration considerably. The observations are analysed then and the final conclusions are presented.

Dynamic analysis of laminated composite skew plates with cut-out

The aim of the present paper deals with free vibration analysis of laminated composite skew plates with single and multiple cut-outs. For complete understanding of the dynamic behavior of laminated skew plates with cut-out a numerical analysis has been carried out by developing a computer code in FOTRAN. Special attention is drawn on the formulation of mass matrix by considering effect of rotary inertia. The results obtained by the finite element formulation using nine noded isoparametric plate bending element are validated by comparing the results from relevant published literature. Few new results on laminated skew plates with cut-out have been presented.

Buckling optimization of variable-stiffness composite panels based on flow field function

Due to the non-uniform in-plane stress distribution, variable-stiffness panel with curvilinear fiber paths is a promising structural concept for cutout reinforcement of composite structures under axial compression, due to the more diverse tailorability opportunities than simply choosing the best straight stacking sequence. However, traditional representation methods of curvilinear fiber path are usually not flexible for cutout reinforcement. In this study, the flow field function containing a uniform field and several vortex fields is utilized to represent the fiber path due to its inherent non-intersect and orthotropic features, and a bi-level optimization framework of variable-stiffness panels considering manufacturing constraints is then proposed. A typical rectangular composite panel with multiple cutouts is established to demonstrate the advantage of proposed framework by comparison with other fiber path functions. Results indicate that the flow fiber path only needs few variables to finely represent the fiber path, which can provide satisfying and manufacturable fiber paths by combination use of curvature constraint.

Simultaneous buckling design of stiffened shells with multiple cutouts

ABSTRACTBuckling is usually initiated from a local region near the cutout for cylindrical stiffened shells under axial compression, and then the evolution of buckling waves is governed by the combined effects of local and global stiffness, which limit the load-carrying capacity. Therefore, a simultaneous buckling pattern is crucial for improving the structural efficiency. In this study, a multi-step optimization strategy for the integrated design of near and far fields away from cutouts is proposed, and the convergence criterion of buckling optimization is improved as a deformation-based index. The numerical implementation of the asymptotic homogenization method is utilized to construct an efficient finite element model for post-buckling analysis. A 5 m diameter stiffened shell in a launch vehicle demonstrates that the proposed framework can provide a simultaneous buckling design with high structural efficiency in an efficient manner. Both the buckling deformations and stress of the optimum design are more uniform compared to other optimum designs.

Integrated optimization of hybrid-stiffness stiffened shells based on sub-panel elements

A concept of hybrid-stiffness stiffened shell is proposed based on sub-panel elements to achieve a simultaneous buckling pattern, which can provide enhanced design flexibility to fully explore the load-carrying capacity of structures. Then, a novel hybrid model is established to improve the computational efficiency of post-buckling analysis for stiffened shells, where the Numerical Implementation of Asymptotic Homogenization Method is utilized to smear out the stiffeners. On this basis, an integrated optimization framework of sub-panel configurations and weld lands for stiffened shells is presented. Illustrative examples with single and multiple cutouts demonstrate the effectiveness of the proposed framework based on the concept of hybrid-stiffness stiffened shell.