Concurrent multi-scale optimization of hybrid composite plates and shells for vibration

In practical engineering, the design scheme is generally a compromise solution that meets various requirements. In most cases, the traditional optimization method provides a single optimized solution, which may be prone to fail during the subsequent design stage because some unpredictable requirements may be not considered in the preliminary optimization process. For example, maximizing fundamental frequency is generally regarded as the optimization objective for aerospace structures under the vibration environment in the preliminary design stage. However, the optimized solution may fail for strength, buckling, or other requirements during the subsequent detailed design stage. Therefore, it is crucial to provide multiple alternative solutions for insurance. In this paper, a diverse discrete material optimization (DDMO) framework is proposed for multi-patch laminates. It can optimize the material topology layout and fiber orientations of composite structures simultaneously and provide multiple alternative solutions that have diversity in design space and different potential performance. In this paper, a diversity index for discrete variables is proposed and the discrete material optimization (DMO) method with the diversity index constraint is employed to perform the DDMO. Two illustrative examples are used to verify the effectiveness of the proposed optimization framework, including a simple example of a composite plate and a complex engineering example of an S-shaped curved shell. Results indicate that, the proposed method can provide multiple diverse alternative solutions with similar performance in the optimization objective, which are verified to have better potential performance than the single solution by the traditional single design method. Moreover, multiple design options by the diverse optimization method can contribute to reducing the probability of redesign and shortening the design cycle.

Application of natural fibre based composite plate in retrofitting of structure is the current interest of construction industry. This paper presents the finding of an experimental study on jute rope fibre hybrid composite plates for potential application in shear strengthening of RC beam. In the experimental programme, hybrid composite plates had been fabricated using jute rope and carbon fibres with five different mixes i.e. 45% jute rope with 0% carbon; 43% jute rope with 2.5% carbon; 41% jute rope with 5% carbon; 41% jute rope with 7.5% carbon and 39% jute rope with 10% carbon.The physical and mechanical properties of the fabricated hybrid composite plates were thenexperimentally investigated. Results showed thatcarbon contents had an influence to enhance the tensile strength of the plates. Hybrid composite plate with 10% carbon content had shown 170% higher tensile strength as compared to that of plate without carbon fibre. The carbon content also had enhanced the modulus of elasticity of plates. Higher percentage of carbon had shown higher tensile strength and modulus of elasticity of hybrid composite plates.All fabricated plates had linear elastic properties under tension. The density of plates increased with the increasing of carbon content in composite plates. The research findings indicated that the developed hybrid composite jute rope could be used for shearstrengthening of reinforced concrete beam.

This work is intended to characterize the mechanical behavior of hybrid carbon–glass composite plates under combined loading of bending and torsion, and to determine the optimal ply fiber orientations to minimize the maximum out-of-plane displacement under such loading conditions. Hybrid composite plates were manufactured with 10 plies each and different stacking sequences using hand lay-up, with carbon fiber and glass fiber reinforcements in an epoxy matrix. Two experimental setups (involving two distinct boundary conditions) are here considered to test the composite plates, both simulating combined loading of bending and torsion. Numerical simulations of the experimental tests were performed in ABAQUS® and validated with the experimental data. Using the ply fiber orientations as design variables, the hybrid composite plates were then optimized using global and local optimization using direct search (GLODS). The objective function of minimization of the maximum out-of-plane displacement is carried out through an interactive cycle between GLODS and ABAQUS®. Specimens of three optimized laminates were also manufactured for experimental validation. The optimization process contributed to improve the performance of the hybrid composite plates in more than 30% when compared to some non-optimized plates.

Thick-section AS4-graphite/E-glass/PPS hybrid composites: Part II. Flexural response

Single-kenaf fiber-reinforced polymer composites are typically characterized by relatively low strength and stiffness properties that make them unsuitable for structural applications. However, they are lightweight, economical, and ecofriendly. This paper presents a study on the manufacturing and mechanical characterization of bidirectional kenaf (K) fiber-reinforced epoxy composites hybridized with carbon (C) fibers in various stacking sequences and the effects of hybridization on salient physical and mechanical properties. Single and hybrid fiber composites were fabricated utilizing the vacuum infusion molding technique. The density, tensile, flexural, and interlaminar shear properties in hybrid composites increased significantly when carbon fiber volume increased from 9% to 16%. Stacking sequences in a hybrid affected the mechanical properties of the composites. The highest tensile strength and modulus were shown by the seven-layer hybrid composite with an alternate K/C stacking sequence and C layers as skin layers, i.e., C/K/C/K/C/K/C, among all tested hybrid composites. Sandwich design in the hybrid (C2/K3/C2) had higher flexural strength (+300%), flexural modulus (+414%), interlaminar shear strength (+278%), lower water absorption (−46%), and thickness swelling (−30%) compared to single-fiber kenaf/epoxy composites. Density increased by 5% in hybrid composites. The highest fracture toughness (+134%) was achieved using the dual sandwich design structure hybrid (C/K2/C2/K2/C). The developed composite has applications in stairways, walkways, and bridges.

This paper studies two-scale concurrent topology optimization with multiple micro heterogeneous materials subject to volume constraints. Unlike the existing work on concurrent two-scale optimization where only one material with optimal microstructure is used or that with multiple micro material where each material is distributed in a number of prescribed geometrical domains, selection of micro heterogeneous materials in this work is based on direction of principal stresses in macro structure. For a structure composed of m micro materials, the macro elements are classified into m categories according to their principal stress direction and each category is assigned with a uniform micro material. The interpolation scheme for macro elements is based on Discrete Material Optimization (DMO), where each element is assigned with m macro design variables. The categorization process of the macro structure is achieved by proper modification of volume constraints, where the macro design variables are multiplied by penalty functions. The penalty functions make it uneconomical for the usage of micro materials, which do not correspond to the principal stress direction of their macro element. The macro structure and micro material are connected through effective property, which is calculated through novel numerical implementation of asymptotic homogenization method (NIAH). Both macro structure and micro materials are optimized concurrently and analytical sensitivities are calculated with adjoint method. One minimum compliance numerical example of an L-bracket subject to volume constraints, where one micro material correspond to macro domain with principal stress angle near 0 or 90 degrees and another correspond to that with principal stress angle near 45 or 135 degrees, is presented to show the potential of the proposed method.

The present article deals with the vibration and damping analysis of functionally graded carbon nanotubes reinforced hybrid composite (FG-CNTRHC) shell structure which consists of conventional carbon fiber as reinforcing phase and single-walled carbon nanotubes based polymer as matrix phase. The Eshelby–Mori–Tanaka approach in conjunction with strength of material approach is implemented to obtain the material properties of FG-CNTRHC structures. The material properties of FG-CNTRHCs are assumed to be graded through the thickness direction according to power law distributions of the volume fraction of carbon fibers and fiber orientations. An eight node shell element considering transverse shear effect according to Mindlin’s hypothesis has been formulated for finite element modelling and analysis of such functionally graded hybrid composite shell structures. The formulation of shell midsurface in an arbitrary curvilinear coordinate system based on the tensorial notation also presented. The Rayleigh damping model has been implemented in order to study the effects of carbon nanotubes (CNTs) on damping capacity of such hybrid shell structures. Different types of spherical shell panels have been analyzed in order to study the time and frequency responses. The influences of CNTs, carbon fiber, geometry of the shell, power law index and material distributions on the vibration damping characteristics of FG-CNTRHC shell structures have also been presented and discussed. Various types of FG-CNTRHC shell structures (such as spherical, ellipsoidal, doubly curved and cylindrical) have been analyzed and discussed in order to comparative studies in terms of settling time, first resonant frequency and absolute amplitude corresponding to first resonant frequency and the effects of CNTs on vibrations responses of such shell structures are also presented.

ABSTRACTFinite periodic layout for multicomponent systems signifies a compelling design strategy for constructing complex larger structures through assembling repeating representative unit‐cells with various orientations. In addition to better transportability, handleability and replaceability, design with structural segmentation has been considered particularly valuable for additive manufacturing of large workpiece due to limited printing dimension of machine. However, existing design optimization of periodic structures has been largely restricted to simple translational placements of unit‐cells, sophisticated tessellation with differently oriented topological unit‐cells remains underexplored. This paper presents an efficient and adaptable topology optimization framework for concurrently optimizing periodic structures comprised of repeating topological unit‐cells and their tailored orientations. By introducing a weighting factor associated with different orientation states of unit‐cells, a dominant orientation for each unit‐cell can gradually emerge in the course of optimization process. The proposed procedure combines the solid isotropic material with penalization (SIMP) model for topology optimization of unit‐cell and the discrete material optimization (DMO) technique for the optimization of its orientation. The optimization objective is to minimize structural compliance subject to volume fraction constraint. Through sensitivity analysis, optimality criteria can be applied to simultaneously optimize a representative unit‐cell (RUC) topology and the orientation weighting factors in the periodic macrostructure. Several 2D and 3D examples are investigated to demonstrate significant enhancement in compliance reduction of up to 34% compared to conventional periodic design without orientation optimization. This represents a notable improvement in finite periodic structural optimization, particularly leveraging the topology optimization to tailor unit‐cell orientation rather than relying on brute‐force search approaches. Our methodology paves a new avenue for designing more efficient and readily manufacturable lightweight structures with enhanced performance metrics.

This research discourse presents the development of a holistic mathematical model that is dedicated to showcase a set of analytical expressions for predicting global stiffness (axial stiffness, bending stiffness) and a material response characterization based on ply-per-ply in-plane stress investigations relevant to open-celled multidirectional curved cylindrical shell configurations. Additionally, the analytical model is shown to present the capability to mathematically determine the location of the centroid for thin-walled, composite cylindrical shells. The resulting centroidal expression for a composite system is essentially shown to be a primary function of material properties, composite stacking sequence, fiber orientation angle and the structural geometry as opposed to metal counterparts whose centroidal point is solely governed by their geometry. Analytical stress estimates are computed for thin-walled curved cylindrical shell constructions that are subjected to typical tension and longitudinal bending type loading conditions applied at the centroid under the presence and absence of a uniformly distributed thermal loading environment. A broad parametric investigation on the in-plane ply stresses (σx,σy,τxy) are conducted via choosing three fundamental parameters namely; varying mean radius of curvature, changing laminate thickness-to-mean radius ratio and increasing laminate thickness respectively. Three preferentially tailored variabilities in ply stacking sequence are established from a [(±45° / 0°]s symmetric-balanced composite lay-up to illustrate the effects on ply stresses. An ANSYS based finite element analysis scheme is employed to numerically determine the location of centroid and further substantiate the analytically acquired centroid predictions including and excluding the effects of temperature. The centroidal point is identified and its location is progressively reported for a fully open cross-sectioned curved strip to a fully closed cylindrical composite tube configuration by examining their distribution pattern as a function of circumferential arc angle (2α). FE tool is additionally utilized to compare the analytical stiffness predictions and analyze the validity of the in-plane analytical stress estimates. Excellent agreement is achieved in comparison between analytical solutions and computationally generated FE results. The central goal of this work is to demonstrate the potential of the formulated mathematical framework in accurately predicting the key mechanical attributes that dictates the structural behavior of curved composite shell members. This analytical model is designed to serve as a robustly efficient tool towards assisting structural design engineers in quickly gaining a broad fundamental understanding on the physical characteristics and structural response of such configurations by accurately conducting simple parametric studies during preliminary design phase prior to performing complex FE analyses.

Many studies were directed toward understanding damage patterns in composite laminates and determining the damage development sequence upon high velocity impact. Damage accumulation depends on projectile velocity and on a number of other parameters, so that it is not possible to set strict limits between the different regimes. However, experiments show that, for a given set of experimental conditions where the impact speed is the only variable, there is a certain threshold velocity below which no detectable damage occurs. Above the threshold velocity, no surface damage is observed except for a small indentation at the contact point, but significant internal damage consisting of delaminating and matrix cracks is introduced. As the impact velocity increases further, surface damage due mainly to fiber breakage is introduced. For very high speeds, the target does not have time to deform, and perforation occurs, leaving a clean hole in the sample. The objective of this study is to develop a mathematical model that corresponds to the deformed geometry under high velocity impact applications for composite laminates. A total of 100 tests were conducted on composite laminates, struck by cylindrohemispherical projectiles at normal incidents with velocities up to about 100 mls. The types of materials, used this study, are AS4/3051, IM7/5250 CarbonlEpoxy and TI003 Glass/Epoxy. The strain energy was obtained by derivation of the proposed deflection function. The strain energy was plotted with respect to the deflection of the mid-plane and, then correlated through dynamic correlation factors to actual kinetic energy during the impact. The dynamic correlation factors were determined using a genetic algorithm regression analysis. Two types of materials were tested, namely plain graphite composites and hybrid composites. The growth of the delamination and also the effect of varying the stacking sequence were investigated for the different type of materials and various orientations. The mathematical model appears to provide a reasonable representation of the deformation of composite laminates during the penetration by a cylindro-hemispherical projectile. Furthermore, hybrid composites appear to provide more resistance to the impact, whereas plain composites have less resistance with respect to the higher velocities. It was concluded that, the change of the material in a hybrid composite affects the growth of the damaged area and also reduces the impact penetration resistance. Hence, IM7/E-Glass hybrid has a higher resistance to the penetration. Measurements of the energy levels of the hybrid composites indicated that they offer the highest resistance to ballistic perforation. The hybrid composites perforated at velocities between 77 mls and 83 (mls), whereas the graphite composites perforated at velocities between 48 m/s and 59 (mls). The higher perforation resistance is attributed to the reduced level of delamination generated during the impact, and also the addition of the E-Glass, which was capable of absorbing more energy during the impact. In studying the graphite composites, the best orientation in terms of the stacking sequence was found to be [(45, -45, 0, 90) 2 ] S , which indicates that this stacking sequence withstand higher velocity and hence absorbs more energy during the impact. Therefore, the quasi-isotropi corientation [(45, -45, 0, 90) 2 ] S is best for impact resistance if a laminate is not combined with E-Glass. The ballistic-limit velocity prior to perforation for the Quasi-isotropic laminate was measured as 58.9 m/s. This is a significant increase compared to the other plain graphite samples. The energy required for the complete perforation is approximately 48% higher in this stacking sequence as compared to other plain Graphite specimens. It was also found that the energy absorption capability is reduced significantly in the cross-ply laminates. The penetration resistance of the [(0,90,0,90) 2 ] S laminate and the energy required for perforation are approximately 50% less than the other plain graphite specimens.

Many studies were directed toward understanding damage patterns in composite laminates and determining the damage development sequence upon high velocity impact. Damage accumulation depends on projectile velocity and on a number of other parameters, so that it is not possible to set strict limits between the different regimes. However, experiments show that, for a given set of experimental conditions where the impact speed is the only variable, there is a certain threshold velocity below which no detectable damage occurs. Above the threshold velocity, no surface damage is observed except for a small indentation at the contact point, but significant internal damage consisting of delaminating and matrix cracks is introduced. As the impact velocity increases further, surface damage due mainly to fiber breakage is introduced. For very high speeds, the target does not have time to deform, and perforation occurs, leaving a clean hole in the sample. The objective of this study is to develop a mathematical model that corresponds to the deformed geometry under high velocity impact applications for composite laminates. A total of 100 tests were conducted on composite laminates, struck by cylindrohemispherical projectiles at normal incidents with velocities up to about 100 mls. The types of materials, used this study, are AS4/3051, IM7/5250 CarbonlEpoxy and TI003 Glass/Epoxy. The strain energy was obtained by derivation of the proposed deflection function. The strain energy was plotted with respect to the deflection of the mid-plane and, then correlated through dynamic correlation factors to actual kinetic energy during the impact. The dynamic correlation factors were determined using a genetic algorithm regression analysis. Two types of materials were tested, namely plain graphite composites and hybrid composites. The growth of the delamination and also the effect of varying the stacking sequence were investigated for the different type of materials and various orientations. The mathematical model appears to provide a reasonable representation of the deformation of composite laminates during the penetration by a cylindro-hemispherical projectile. Furthermore, hybrid composites appear to provide more resistance to the impact, whereas plain composites have less resistance with respect to the higher velocities. It was concluded that, the change of the material in a hybrid composite affects the growth of the damaged area and also reduces the impact penetration resistance. Hence, IM7/E-Glass hybrid has a higher resistance to the penetration. Measurements of the energy levels of the hybrid composites indicated that they offer the highest resistance to ballistic perforation. The hybrid composites perforated at velocities between 77 mls and 83 (mls), whereas the graphite composites perforated at velocities between 48 m/s and 59 (mls). The higher perforation resistance is attributed to the reduced level of delamination generated during the impact, and also the addition of the E-Glass, which was capable of absorbing more energy during the impact. In studying the graphite composites, the best orientation in terms of the stacking sequence was found to be [(45, -45, 0, 90) 2 ] S , which indicates that this stacking sequence withstand higher velocity and hence absorbs more energy during the impact. Therefore, the quasi-isotropi corientation [(45, -45, 0, 90) 2 ] S is best for impact resistance if a laminate is not combined with E-Glass. The ballistic-limit velocity prior to perforation for the Quasi-isotropic laminate was measured as 58.9 m/s. This is a significant increase compared to the other plain graphite samples. The energy required for the complete perforation is approximately 48% higher in this stacking sequence as compared to other plain Graphite specimens. It was also found that the energy absorption capability is reduced significantly in the cross-ply laminates. The penetration resistance of the [(0,90,0,90) 2 ] S laminate and the energy required for perforation are approximately 50% less than the other plain graphite specimens.

Influence of layering sequences on tensile properties of hybrid woven Jute/Ramie fibre reinforced polyester composites

Concurrent multi-material and multi-scale design optimization of fiber-reinforced composite material and structures for minimum structural compliance

Developing biocomposites by hybridization, which is the combination of two or more materials, can be a potential solution for improving material recyclability and sustainability. This study focuses on creating a hybrid biocomposite reinforced with cotton-blended pineapple leaf fibre (PALF) fabric (174 GSM) and jute fibre fabric (265 GSM) which are thrown away by textile factories. The mechanical, moisture absorption, and vibration characteristics of four stacking sequences of hybrid composites and two unhybridized composites were analyzed. Results indicated that hybridization improved tensile and flexural characteristics compared to pineapple leaf fibre reinforced polymer (PFRP) composites. The jute fibre reinforced polymer (JFRP) composite exhibited the maximum tensile strength of 35.16 MPa, while the hybrid composites achieved a maximum of 32.16 MPa. Among the hybrid composites, jute layers on the outer plies (4P5J-2) demonstrated the maximum tensile modulus of 1.315 GPa. Additionally, the hybrid composite with three layers of jute plies between alternating layers of jute-pineapple plies showed the highest elongation at 15.94%. Among the hybrids, alternate stacking of jute/PALF plies (4P5J-1) gave a maximum flexural strength of 44.36 MPa, which is similar to JFRP (44.91 MPa) and a 78.57% increase in flexural modulus compared to PFRP composite, despite having the lowest tensile strength. Although the JFRP composite exhibited the highest impact strength, the hybrids still outperformed the PFRP composites. With hybridization, moisture absorption decreased, with a maximum of 29.50% compared to the JFRP composite. Furthermore, due to the spiral-like orientation of the yarns, stacking PALF plies on the outside can cause critical damping. Therefore, it is shown in this paper that both hybridization and stacking sequence can significantly influence composite performance. These findings also implies the utilization of textile industry's natural fibres to develop hybrid composites for automotive applications, like brake and accelerator pedals, for a greener future and effective waste material utilization.

Recently, vehicle parts such as center pillars and impact beams used in automobiles have been requiring materials that satisfy both high strength and impact absorption. Therefore, in this study, the applicability of the forming process of CR340 (cold rolled steel sheet)/carbon fiber reinforced plastic (CFRP) hybrid composites which are a bonded material of cold rolled steel sheet having excellent formability and carbon fiber prepreg having high strength and high collision absorption in the vehicle parts was investigated. Hybrid composites are fabricated by stacking CFRP prepreg on a cold rolled steel sheet (CR340) with Zn coating. Bonding materials were used at the interface between the CFRP prepreg and steel sheet. This study investigated the formability and fiber orientation of CR340/CFRP hybrid composite after deep drawing. Square cup deep drawing tests were conducted with various process parameters to evaluate the formability of CR340/CFRP hybrid composite. The square deep drawing process parameters and the thinning rate at each position of the drawing product were measured, and the various problems encountered during the deep drawing process were reviewed with the thermal flow of epoxy. Experimental data between the forming depth and blank holding force was introduced with CFRP/CR340 with Zn coating sheet hybrid composite. The thickness variations of the materials and the fiber orientations were observed using cross sections at each position. Void and delamination defects were observed at the die round and were discussed in detail.