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The purpose of this study is to investigate the strain rate effect on the problem of low-velocity impact (LVI) on a beam, including silicon nitride and stainless steel materials.

Based on the nonlinear Hertz impact mechanism, the energies related to the impactor and the beam are written, and motion equations are derived using the Lagrangian mechanics and Ritz method. The strain rate term is represented as a damping matrix in the equations of motion. In the issue of LVI on the silicon nitride and stainless steel beam, the effect of internal viscous damping coefficient in simply–simply and clamped–free boundary conditions are studied. Also, the influence of the volume fraction index in the range between zero and one and greater than one on the impact response is investigated.

The results make it clear that the strain rate parameter had little effect on the response in LVI. Also, an increase in the volume fraction index has led to a decrease in the contact force and an increase in the rebound velocity of the impactor.

The effect of strain rate on LVI is theoretically studied in this paper, while in most of the papers, this effect is investigated experimentally and numerically.

Engineering composite laminates/structures are usually subjected to complex and variable loads, which result in interlayer delamination damage. However, damaged laminate may cause the whole structure to fail before reaching the design level. Therefore, the purpose of this paper is to develop an equivalent model to effectively evaluate compressive residual strength.

In this paper, taking carbon fiber reinforced composite T300/69 specimens as the study object, first, the compressive residual strength under different impact energy is obtained. Then, zero-thickness cohesive elements, Hashin failure criteria and Camanho nonlinear degradation scheme are used to simulate the full-process simulation for compression after edge impact (CAEI). Lastly, based on an improved Whitney–Nuismer criterion, the equation of edge hole stress distribution, characteristic length and compressive residual strength is used to verify the correctness of the equivalent model.

An equivalent relationship between the compressive residual strength of damaged laminates and laminates with edge hole is established. For T300/69 laminates with a thickness of 2.4 mm, the compressive residual strength after damage under an impact energy of 3 J is equivalent to that when the hole aperture R = 2.25 mm and the hole aperture R = 9.18 mm when impact energy is 6 J. Besides, the relationship under the same size and different thickness is obtained.

The value of this study is to provide a reference for the equivalent behavior of damaged laminates. An equivalent model proposed in this paper will contribute to the research of compressive residual strength and provide a theoretical basis for practical engineering application.

The purpose of this paper is to investigate the nonsimultaneous impact of three impactors with spherical tip on the response of a low-velocity impact on a beam.

In this research, the third-order shear deformation theory of the beam with hyperbolic shear-strain function is used. Hamilton’s principle is applied to derive the motion equations. To simulate nonsimultaneous impacts, by using the Hertz nonlinear contact law, the contact of the impactors with different times is simulated. Comparisons with other articles are carried out in the one impactor form.

In the parametric study, the histories of the contact force and displacement of the beam are investigated in the presence of only one impactor in the center of the beam and also in the presence of three impactors, one in the center of the beam and the other two around the first impactor with a delay. One of the important and noteworthy points is that the presence of two impactors with a delay causes the maximum contact force and contact time to decrease and the maximum displacement of the beam center to increase.

The original point of this paper is what is the difference between the impact response of one projectile and three nonsimultaneous projectiles on the beam.

This article focuses on the low-velocity impact (LVI) output of carbon nanotubes (CNTs)’ reinforcement circular plates, considering agglomeration size effect and clumping of CNTs’ inner side of the agglomerations.

A representative volume element (RVE) is used to determine the nanocomposite properties reinforced with agglomerated CNTs with random orientation. First-order shear deformation theory (FSDT) is used to obtain the motion equations of LVI analysis. These equations are handled by developing a Ritz method and Lagrangian mechanics. To extract the mass and stiffness matrices, terms with second and higher degrees are ignored.

Formulation validation is performed by providing various examples, including comparisons with other research and ABAQUS FE code. The effects of agglomeration size, clumping of CNTs’ inner side of the agglomerations, CNT volume fraction and impact location on the responses of impact load, projectile displacement and plate deflection are analytically studied. These achievements illuminate how the influence of agglomeration size is very small on the impact response. Also, the influence of clumping of CNTs’ inner side of the agglomerations is significant, and as it increases, the displacement values and impact time increase, and the impact force decreases.

In this article, to avoid additional calculations, the parameters of the mass matrix and the stiffness coefficients are linearized to obtain the equations of motion of the impact on the circular plate.

The purpose of this study is to model the theory of the low-velocity impact (LVI) process on sandwich beams consisting of flexible cores and face sheets reinforced with functionally graded carbon nanotubes (CNTs).

A series of parameters derived from molecular dynamics are used to consider the size scale in the mixture rule for the combination of CNTs and resin. A procedure involving the use of the first-order shear deformation theory of the beam is used to provide the displacement field of the sandwich beam. The energy method and subsequently the generalized Lagrange method are used to derive the motion equations. Due to the use of Hertz’s nonlinear theory to calculate the contact force, the equations of motion are nonlinear. Validation of the problem is carried out by comparing natural frequencies with other papers.

The influence of a series of parameters such as CNTs distributions pattern in the face sheets, the influence of the CNTs volume fraction and the influence of the core thickness to the face sheets thickness ratio in the issue of LVI on sandwich beams with clamped-clamped boundary conditions is investigated. The result shows that the type of CNTs pattern in the face sheet and the CNTs volume fraction have a very important effect on the answer to the problem, which is caused by the change in the value of the Young’s modulus of the beam at the contact surface. Changes in the core thickness to the face sheets thickness ratio has little effect on the impact response.

Considering the important application of sandwich structures in vehicles, aviation and ships, in this research, sandwich beams consisting of flexible core and CNTs-reinforced face sheets are investigated under LVI.

The purpose of this study is to extract the response of the simultaneous low-velocity impact of multiple impactors on a porous functionally graded (FG) aluminum plate.

To design a porous FG structure, a series of functions are applied using the porosity coefficient, and mechanical properties including Young’s modulus, shear modulus and the density of the porous structure are presented as a function of the axis placed in the direction of the plate thickness. The first-order shear deformation theory of the plate is used. To simulate the contact process between each impactor and the plate, a nonlinear Hertz contact force is considered for that impactor independently.

ABAQUS finite element software is used for the verification process of the theorical equations. The effects of porous function type, radius and initial velocity of impactor are investigated for the simultaneous impact of five impactors on porous FG aluminum plate with a simply supported boundary condition. Histories of contact force and displacement of the impactor placed in the center of the beam are analyzed in detail with the changes of the mentioned parameters.

Due to the advantages of porous aluminum plate such as high energy absorption and low weight, such structures may be subjected to the simultaneous impact of multiple impactors, which is studied in this research.

The purpose of this article is to investigate the porosity-dependent impact study of a plate with Winkler–Pasternak elastic foundations reinforced with agglomerated carbon nanotubes (CNTs).

Based on the first-order shear deformation plate theory, the strain energy related to elastic foundations is added to system strain energy. Using separation of variables and Lagrangian generalized equations, the nonlinear and time-dependent motion equations are extracted.

Verification examples are fulfilled to prove the precision and effectiveness of the presented model. The impact outputs illustrate the effects of various distribution of CNTs porosity functions along the plate thickness direction, Winkler–Pasternak elastic foundations and different boundary conditions on the Hertz contact law, the plate center displacement, impactor displacement and impactor velocity.

This paper investigates the effect of Winkler–Pasternak elastic foundations on the functionally graded porous plate reinforced with agglomerated CNTs under impact loading.

The purpose of this study is to find the best geometries among the cylindrical, enamel and honeycomb geometries based upon the mechanical properties (tensile test, compression test and shear test). Further this obtained geometry could be used to fabricate products like exoskeleton and its supporting members.

The present research focuses on the mechanical testing of cylindrical, enamel and honeycomb-shaped parts fabricated through multi-jet printing (MJP) process with a wall thickness of 0.26, 0.33, 0.4 and 0.66 mm. The polymer specimens (for tensile, compression and shear tests) were fabricated using a multi-jet fusion process. The experimental results were compared with the numerical modelling. Finally, the optimal geometry was obtained, and the influence of wall thicknesses on various mechanical properties (tensile, compression and shear) was studied.

In comparison to cylindrical, enamel structures the honeycomb structures required less time to fabricate and had lower tensile, compressive and shear strengths. The most efficient geometry for fully functional parts where tensile, compressive and shear forces are present during application – cylindrical geometry is preferred followed by enamel, and then honeycomb. It was found that as the wall thickness of various geometries was increased, their ability to withstand tensile, compressive and shear loads also enhanced. The enamel shape structure exhibits greater strain energy storage capacity than other shape structures for compressive loads, and the strength to resist the compressive load will be lower. In the case of cylindrical geometries for tensile loading, the resisting area toward the loading will be higher in comparison to honeycomb- and enamel-based structures. At the same time, the ability to store the stain energy is less. The results of the tensile, compression and shear load finite element analysis using ANSYS are in agreement with those of the experiments.

From the insight of literature review, it is found that a wide range of work is done on fused deposition modeling (FDM) process. But in comparison to FDM, the MJP provide the better dimensional accuracy and surface properties (Lee et al., 2020). Therefore, it is observed that past research works not incorporated the effect of wall thickness of the embedded geometries on mechanical properties of the part fabricated on MJP (Gibson, n.d.). Hence, in this work, effect of wall thickness on tensile, compression and shear strength is considered as the main factor for the honeycomb, enamel and cylindrical geometries.

In this paper, an attempt is made to obtain buckling loads, ultimate bearing capacity and other required structural characteristics of grid structure panels. The numerical method for post-buckling behavior analysis of panels involving multiple invisible damages is also presented.

In this paper, two bidirectional stiffened composite panels are manufactured and tested. Multiple discrete invisible damages are introduced in different positions of the stringers, and the experimental and simulation investigation of buckling and post-buckling were carried out on the damaged stiffened panels.

The simulation load–displacement curves are compared with the experimental results, and it is found that the simulation model can well predict the occurrence of buckling and failure loads. The strain curve shows that the rate of strain change at the damaged site is greater than that at the undamaged site, which reflects that the debond is more likely occurred at the damaged site. The simulation verifies that the panel is usually crushed due to matrix compression and fiber–matrix shear.

In this paper, post-buckling tests and numerical simulations of bidirectional stiffened composite panels with impact damage were carried out. Two panels with four longitudinal stringers and two transverse stringers were manufactured and tested. The buckling and post-buckling characteristics of the grid structure are obtained, and the failure mechanism of the structure is explained. This is helpful for the design of wall panel structure.

The purpose of this paper is to introduce a methodology aimed to detect debonding induced by low impacts energies in typical aeronautical structures. The methodology is based on high frequency sensors/actuators system simulation and the application of elliptical triangulation (ET) and probability ellipse (PE) methods as damage detector. Numerical and experimental results on small-scale stiffened panels made of carbon fiber-reinforced plastic material are discussed.

The damage detection methodology is based on high frequency sensors/actuators piezoceramics system enabling the ET and the PE methods. The approach is based on ultrasonic guided waves propagation measurement and simulation within the structure and perturbations induced by debonding or impact damage that affect the signal characteristics.

The work is focused on debonding detection via test and simulations and calculation of damage indexes (DIs). The ET and PE methodologies have demonstrated the link between the DIs and debonding enabling the identification of position and growth of the damage.

The debonding between two structural elements caused in manufacturing or in-service is very difficult to detect, especially when the components are in low accessibility areas. This criticality, together with the uncertainty of long-term adhesive performance and the inability to continuously assess the debonding condition, induces the aircrafts’ manufacturers to pursuit ultraconservative design approach, with in turn an increment in final weight of these parts. The aim of this research’s activity is to demonstrate the effectiveness of the proposed methodology and the robustness of the structural health monitoring system to detect debonding in a typical aeronautical structural joint.