Transient Dynamic Loading Research Articles

Bending analyses of 1D orthorhombic quasicrystal plates

The meshless Petrov–Galerkin method (MLPG) is applied to plate bending analysis in 1D orthorhombic quasicrystals (QCs) under static and transient dynamic loads. The Bak and elasto-hydrodynamic models are applied for phason governing equation in the elastodynamic case. The phason displacement for the orthorhombic QC in the first-order shear deformation plate theory depends only on the in-plane coordinates on the mean plate surface. Nodal points are randomly distributed over the mean surface of the considered plate. Each node is the center of a circle surrounding this node. The coupled governing partial differential equations are satisfied in a weak-form on small fictitious subdomains. The spatial variations of the phonon and phason displacements are approximated by the moving least-squares (MLS) scheme. After performing the spatial MLS approximation, a system of ordinary differential equations (ODEs) for nodal unknowns is obtained. The system of the ODEs of the second order is solved by the Houbolt finite-difference scheme. Our numerical examples demonstrate clearly the effect of the coupling parameter on both static and dynamic phonon/phason deflections.

Analysis of Statics and Transient Responses on Automotive Gearbox Casing

The three-dimensional solid modeling is built based on some Automobile gearbox Product, the dangerous working conditions of static load are analyzed. On the basis of ADAMS, transient dynamic loads of gearbox at different working gears are found out. The finite element analysis modeling of gearbox casing is built. The static displacement and the stress distribution of gearbox casing are obtained, and the static strength and stiffness are evaluated. The eigenvalues of vibration of gearbox casing are solved, the coupling relationship of the excitation frequency and the gearbox casing natural frequency is analyzed. Based on the transient dynamic analysis of gearbox casing at the first gear and the reverse gear, the evaluations of the dynamic strength and dynamic stiffness are obtained and the weak position of structure is found out, which provides the beneficial information for the further study on the design of the fatigue and reliability of gearbox casing.

Analyses of functionally graded plates with a magnetoelectroelastic layer

A meshless local Petrov–Galerkin (MLPG) method is presented for the analysis of functionally graded material (FGM) plates with a sensor/actuator magnetoelectroelastic layer localized on the top surface of the plate. The Reissner–Mindlin shear deformation theory is applied to describe the plate bending problem. The expressions for the bending moment, shear force and normal force are obtained by integration through the FGM plate and magnetoelectric layer for the corresponding constitutive equations. Then, the original three-dimensional (3D) thick-plate problem is reduced to a two-dimensional (2D) problem. Nodal points are randomly distributed over the mean surface of the considered plate. Each node is the center of a circle surrounding the node. The weak-form on small subdomains with a Heaviside step function as the test function is applied to derive local integral equations. After performing the spatial MLS approximation, a system of ordinary differential equations of the second order for certain nodal unknowns is obtained. The derived ordinary differential equations are solved by the Houbolt finite-difference scheme. Pure mechanical loads or electromagnetic potentials are prescribed on the top of the layered plate. Both stationary and transient dynamic loads are analyzed.

Shock Waves Impacting Composite Material Plates: The Mutual Interaction

High-performance, fiber-reinforced polymer composites have been extensively used in structural applications in the last 30 years because of their light weight combined with high specific stiffness and strength at a rather low cost. The automotive industry has adopted these materials in new designs of lightweight vehicles. The mechanical response and characterization of such materials under transient dynamic loading caused with shock impact induced by blast is not well understood. Air blast is associated with a fast traveling shock front with high pressure across followed by a decrease in pressure behind due to expansion waves. The time scales associated with the shock front are typically 103 faster than those involved in the expansion waves. Impingement of blast waves on structures can cause a reflection of the wave off the surface of the structure followed by a substantial transient aerodynamic load, which can cause significant deformation and damage of the structure. These can alter the overpressure, which is built behind the reflected shock. In addition, a complex aeroelastic interaction between the blast wave and the structure develops that can induce reverberation within an enclosure, which can cause substantial overpressure through multiple reflections of the wave. Numerical simulations of such interactions are quite challenging. They usually require coupled solvers for the flow and the structure. The present contribution provides a physics-based analysis of the phenomena involved, a critical review of existing computational techniques together with some recent results involving face-on impact of shock waves on thin composite plates.

Meshless Modelling of Laminate Mindlin Plates under Dynamic Loads

Collocation method and Galerkin method have been dominant in the existing meshless methods. A meshless local Petrov-Galerkin (MLPG) method is applied to solve laminate plate problems described by the Reissner-Mindlin theory for transient dynamic loads. The Reissner-Mindlin theory reduces the original three-dimensional (3-D) thick plate problem to a two-dimensional (2-D) problem. The bending moment and the shear force expressions are obtained by integration through the laminated plate for the considered constitutive equations in each lamina. The weak-form on small subdomains with a Heaviside step function as the test functions is applied to derive local integral equations. After performing the spatial MLS approximation, a system of ordinary differential equations of the second order for certain nodal unknowns is obtained. The derived ordinary differential equations are solved by the Houbolt finite-difference scheme as a time-stepping method.

Dynamic cohesive crack propagation modelling using the scaled boundary finite element method

ABSTRACTThis study develops a scaled boundary finite element method (SBFEM)‐based approach for modelling fast cohesive crack propagation in quasi‐brittle materials subjected to transient dynamic loadings. In this approach, the elastic bulk material is modelled by SBFEM subdomains and the cracks by nonlinear cohesive interface finite elements that are automatically inserted by a remeshing procedure. The global equation system is solved using an implicit time integration algorithm. Because all the solutions (displacements, stresses, velocities, accelerations) are semi‐analytical in an SBFEM subdomain, this approach offers a few advantages over other methods, such as accurate calculation of dynamic stress intensity factors and T‐stress without using fine crack‐tip meshes, simpler remeshing, more accurate and efficient mesh mapping, and the need of much fewer degrees of freedom for the same accuracy. The approach is validated by modelling two concrete beams under impact, subjected to mode‐I and mixed‐mode fracture, respectively.

Dynamic Loading on Turbofan Blades Due to Bird-Strike

In the present paper, a hydrodynamic bird material model made up of water and air mixture is developed, which produces good correlation with the measured strain-gauge test data in a panel test. This parametric bird projectile model is used to generate the time-history of the transient dynamic loads on the turbofan engine blades for different size birds impacting at varying span locations of the fan blade. The problem is formulated in 3D vector dynamics equations using a nonlinear trajectory analysis approach. The analytical derivation captures the physics of the slicing process by considering the incoming bird in the shape of a cylindrical impactor as it comes into contact with the rotating fan blades modeled as a pretwisted plate with a camber. The contact-impact dynamic loading on the airfoil produced during the bird-strike is determined by solving the coupled nonlinear dynamical equations governing the movement of the bird-slice in time-domain using a sixth-order Runge-Kutta technique. The analytically predicted family of load time-history curves enables the blade designer to readily identify the critical impact location for peak dynamic loading condition during the bird-ingestion tests mandated for certification by the regulatory agencies.

Elucidating the mechanical behavior of ultra-high-strength concrete under repeated impact loading

The response of concrete to transient dynamic loading has received extensive attention for both civil and military applications. Accordingly, thoroughly understanding the response and failure modes of concrete subjected to impact or explosive loading is vital to the protection provided by fortifications. Reactive powder concrete (RPC), as developed by Richard and Cheyrezy (1995) in recent years, is a unique mixture that is cured such that it has an ultra-high compressive strength. In this work, the concrete cylinders with different steel fiber volume fractions were subjected to repeated impact loading by a split Hopkinson Pressure Bar (SHPB) device. Experimental results indicate that the ability of repeated impact resistance of ultra-high-strength concrete was markedly superior to that of other specimens. Additionally, the rate of damage was decelerated and the energy absorption of ultra-high-strength concrete improved as the steel fiber volume fraction increased.

Gear Defect Modeling of a Multiple‐Stage Gear Train

This study demonstrates the transient and steady state dynamic loading on teeth within a two‐stage gear transmission arising from backlash and geometric manufacturing errors by utilizing a nonlinear multibody dynamics software model. Backlash between gear teeth which is essential to provide better lubrication on tooth surfaces and to eliminate interference is included as a defect and a necessary part of transmission design. Torsional vibration is shown to cause teeth separation and double‐sided impacts in unloaded and lightly loaded gearing drives. Vibration and impact force distinctions between backlash and combinations of transmission errors are demonstrated under different initial velocities and load conditions. The backlash and manufacturing errors in the first stage of the gear train are distinct from those of the second stage. By analyzing the signal at a location between the two stages, the mutually affected impact forces are observed from different gear pairs, a phenomenon not observed from single pair of gears. Frequency analysis shows the appearance of side band modulations as well as harmonics of the gear mesh frequency. A joint time‐frequency response analysis during startup illustrates the manner in which contact forces increase during acceleration.

Blast Testing of Aluminum Foam–Protected Reinforced Concrete Slabs

Aluminum foam is a newly developed mobile and lightweight material with excellent energy absorption capacities. Applying aluminum foam as a sacrificial protection layer on the bearing faces of protected structures can mitigate blast effects on the resistance capacities of structures against impact or blast loading. The aluminum foam undergoes great plastic deformation under transient dynamic loads before becoming fully densified, making it excellent for mitigating blast effects on these structures. In this paper, we conducted quasi-static testing on two types of aluminum foam specimens and obtained the primary parameters for the mechanical properties of aluminum foam specimens. We then used these two types of aluminum foams to protect the reinforced concrete (RC) slabs, and we conducted a series of tests to investigate the performance of the aluminum foam–protected RC slabs against blast loads. We tested a total of five foam-protected slabs and one control RC slab in the blast test program. The test resul...

SIMULAND - A CODE TO ANALYZE DYNAMIC EFFECTS DURING LANDING

The landing gear of an aircraft is part of the aircraft structure. It is the most critical part of the flight mission and also the component that will likely cause the most problems in the aircraft design. The landing gear design combines the best in mechanical, structural and hydraulic design. The designed landing gear should be able to meet the specifications and requirements imposed by the CS23. SIMULAND-01 is a program intended to analyze a reduced model (4-30 DoF) of the aircraft under transient dynamic loads during the landing phase (touchdown).

Evaluation of Surface-Related Pavement Damage due to Tire Braking

ABSTRACT The response of flexible pavement at near-surface is significantly affected by interfacial tire-pavement contact stresses. In addition to highly non-uniform vertical stresses and surface tangential shear stresses at tire-pavement interface, tire braking at an intersection causes additional significant longitudinal contact stresses on the pavement surface. In this paper, the flexible pavement responses to three-dimensional (3-D) tire-pavement contact stresses at various tire rolling conditions were determined using a developed 3-D finite element model. The hot-mix asphalt (HMA) layer was characterized as a viscoelastic material, and the transient dynamic tire loading was simulated using a continuous moving load and implicit dynamic analysis. The analysis matrix includes two typical flexible pavement structures (76 mm and 152 mm HMA thicknesses) and three tire rolling conditions (free rolling at high speed, free rolling at low speed, and braking). The study concluded that the low-speed vehicle load...

Evaluation of Surface-Related Pavement Damage due to Tire Braking

ABSTRACT The response of flexible pavement at near-surface is significantly affected by interfacial tire-pavement contact stresses. In addition to highly non-uniform vertical stresses and surface tangential shear stresses at tire-pavement interface, tire braking at an intersection causes additional significant longitudinal contact stresses on the pavement surface. In this paper, the flexible pavement responses to three-dimensional (3-D) tire-pavement contact stresses at various tire rolling conditions were determined using a developed 3-D finite element model. The hot-mix asphalt (HMA) layer was characterized as a viscoelastic material, and the transient dynamic tire loading was simulated using a continuous moving load and implicit dynamic analysis. The analysis matrix includes two typical flexible pavement structures (76 mm and 152 mm HMA thicknesses) and three tire rolling conditions (free rolling at high speed, free rolling at low speed, and braking). The study concluded that the low-speed vehicle loading and tire braking aggravates the pavement deterioration at an intersection in terms of rutting or shoving in the HMA and surface cracking at the pavement surface. During tire braking, the damage ratios for pavement surface cracking may be as high as 8 to 32 depending on HMA thickness, compared to the normal traffic loading conditions. The tire braking increases the HMA rutting or shoving potential by 2.0 to 2.6 times due to the increased shear strains in two directions. Hence, pavements for intersections should be specified, designed, and constructed differently than regular asphalt pavements to withstand the more severe loading conditions.

Computer-Aided Design and Analysis of a Custom-Engineered Form Milling Cutter

AbstractCustom-Engineered (Special) cutting tools are required for machining complex surfaces or for some specific application. Accurate geometry and design of custom- engineered form milling (CEFM) cutter is needed for its analysis before actual usage. Traditionally, the cutter models are usually defined using two-dimensional conventional nomenclature. This paper presents a precise geometric design model of a brazed insert-based CEFM cutter in terms of three-dimensional (3D) parameters. The proposed model, developed in terms of surface patches employs a methodology that defines the CEFM cutter in terms of 3D rotational angles. Further, an interface is developed to render the proposed 3D CEFM cutter directly in a commercial CAD modeling environment to validate the methodology. The modeled cutter is analyzed using finite element analysis (FEA) tool to study the effects on cutting insert under transient dynamic load conditions during the machining process to verify its design.

Three-dimensional finite element analysis of the stress in abutment periodontal ligament of cantilever fixed bridge under dynamic loads

To analyze the stress distribution in the abutment periodontal ligament of posterior cantilever bridge under transient dynamic loads using a three-dimensional finite element(FE) model. A cantilever bridge using 5, 6 as abutments to restore missing 7 was designed, and its FE model was established and loaded with dynamic loads. The loads were set as 250 N occlusal forces loaded at different positions on the cantilever, and in different directions to simulate the masticatory cycle. FE analysis was conducted on the ANSYS to analyze stress distributions in abutment periodontal ligament under dynamic loads. Stress-time curves were traced to understand the biomechanical behavior of abutment periodontal ligament. With loading and unloading time accumulated, the stress value in the abutment periodontal ligament increased gradually. Loads in lateral direction induced peak value stress in a masticatory cycle. There was little residual stress in the end of unloading phase. The maximum stress concentrated in abutment periodontal ligament adjacent to the missing tooth. Without restoration abutment periodontal ligament was mainly under compressive stress. However, when 7 was restored with a cantilever bridge, tensile stress was shown in the mesial cervical area of 5, Three masticatory cycles were simulated, and stress values in abutment periodontal ligaments increased with the number of masticatory cycles. But the differences of the stress between different masticatory cycles were not significant. In the mastication movement, lateral loads induce maximum stress in abutment periodontal ligament. Cantilever fixed bridge design is more demanding for the periodontal condition of the abutment adjacent to the missing tooth than for the other abutment. When loaded with continuous masticatory force, the stress concentration does not increase significantly. Therefore, cantilever bridge is one of the feasible choices to restore missing lower second molar.

A High Precision Direct Integration Scheme for Nonlinear Dynamic Systems

Based on the high precision direct (HPD) integration scheme for linear systems, a high precision direct integration scheme for nonlinear (HPD-NL) dynamic systems is developed. The method retains all the advantages of the standard HPD scheme (high precision with large time-steps and computational efficiency) while allowing nonlinearities to be introduced with little additional computational effort. In addition, limitations on minimum time step resulting from the approximation that load varies linearly between time-steps are reduced by introducing a polynomial approximation of the load. This means that, in situations where a rapidly varying or transient dynamic load occurs, a larger time-step can still be used while maintaining a good approximation of the forcing function and, hence, the accuracy of the solution. Numerical examples of the HPD-NL scheme compared with Newmark’s method and the fourth-order Runge–Kutta (Kutta 4) method are presented. The examples demonstrate the high accuracy and numerical efficiency of the proposed method.

Estimation of the Relative Density for Honeycomb Panels Subjected to Blast

Sandwich panels give an optimum and proven tools to handle problems related to design and analysis of the structures subjected to blast load. The present work focuses on estimating the relative density of steel honeycomb sandwich panels. These panels can be applied on defense works, homeland security, banks and civilian industries intended to minimize the effects of accidental explosions. Sandwich constructions with metallic hexagonal honeycomb core are utilized in this paper due to its high specific strength and stiffness relative to its weight. Estimating the relative density of the metallic hexagonal honeycomb core based on single degree of freedom and the scaling dimensional and considering the dynamic factor contrived under transient dynamic loads resulted from detonating any amount of TNT at any stand-off distance. The strength and stiffness of simply support honeycomb core panels were evaluated based on boundary condition of strength and deformation. The proposed approach suggested controlling the safety design for those panels.

Acoustic monitoring of superconducting magnet component test and shock simulation of coils

Monitoring of critical components is becoming a more and more important task especially in complex multidisciplinary systems as e.g. the Wendelstein 7-X [L. Wegener et al., Status of Wendelstein 7-X construction, Fusion Engineering and Design, in press; M. Gasparotto et al., The Wendelstein 7-X mechanical structure support elements, Fusion Engineering and Design 74 (2005) 161]. Here especially the superconducting magnetic coil system – comprising, i.a., narrow support elements (NSEs) and bolted connections – is considered. These had been tested in a full-scale test set-up with multi axial loading in the MN range at 77 K and vacuum [B. Heinemann et al., Design of narrow support elements for non planar coils of Wendelstein 7-X, 21st IEEE/NPSS Symposium on Fusion Engineering (SOFE05), Knoxville/USA, 26–9 September 2005, paper 078; D. Hathiramani et al., Full-scale friction test on tilted sliding bearings for Wendelstein 7-X coils, Fusion Engineering and Design, in press]. A smooth sliding of coated surfaces is a major requirement, as non-smooth sliding (stick-slip) excites high mechanical shock loads, which may cause a quench of the superconductor. For an early detection of stick-slip an acoustic monitoring system has been developed and installed. Three sensor types have been compared and data analysis procedures have been developed. It has been shown that acoustic monitoring is possible under such environmental conditions at complex test set-ups and is complementary to standard sensor systems. For the development of the mechanical quench experiment, in which the actual quench sensitivityl to mechanical shock loads is investigated by impact loads, numerical simulations have been performed. For this a semi-analytical model employing a reduced modal state space model of the coil and Hertz’ian theory for the contact formulation has been set-up. Based on experimental and numerical verification it proved to be an appropriate and efficient tool for simulating complex mechanical systems under transient dynamic loading. Finally, a statistical energy based model has been set-up for simulating the propagation of stick-slip shocks within the complex coil system. Concluding, with the developed acoustic monitoring as well as the numerical simulation models two valuable tools for the W7-X development-test projects have been developed.

Analysis and optimization of laminated composite circular cylindrical shell subjected to compressive axial and transverse transient dynamic loads

Optimization is one of the important stages in the design process. In this paper the genetic algorithms method is applied for weight and transient dynamic response and two constraints including critical buckling loads and principle strains optimization of laminated composite cylindrical shells. The multi-objective function seeks the minimum structural weight and transient dynamic response. Nine design variables including material properties (fibre and matrix), volume fraction of fibre, fibre orientation and thickness of each layer are considered. In analytical solution, vibration of composite circular cylindrical shells are investigated based on the first-order shear deformation shell theory. The boundary conditions are assumed to be fully simply support. The dynamic response of the composite shells is studied under transverse impulse and axial compressive loads. The modal technique is used to develop the analytical solution of the composite cylindrical shell. The solution for the shell under the given loading conditions can be found using the convolution integrals. An example of simply supported laminated composite cylindrical shells is given to demonstrate the optimality of the solution obtained by the genetic algorithms technique. Results are shown that the weight coefficient of multi-objective function and the type of the constraints have considerable effect on the optimum weight and dynamic response.

Three dimensional modeling and finite element simulation of a generic end mill

The geometry of cutting flutes and the surfaces of end mills is one of the crucial parameters affecting the quality of the machining in the case of end milling. These are usually represented by two-dimensional models. This paper describes in detail the methodology to model the geometry of a flat end mill in terms of three-dimensional parameters. The geometric definition of the end mill is developed in terms of surface patches; flutes as helicoidal surfaces, the shank as a surface of revolution and the blending surfaces as bicubic Bezier and biparametric sweep surfaces. The proposed model defines the end mill in terms of three-dimensional rotational angles rather than the conventional two dimensional angles. To validate the methodology, the flat end milling cutter is directly rendered in OpenGL environment in terms of three-dimensional parameters. Further, an interface is developed that directly pulls the proposed three-dimensional model defined with the help of parametric equations into a commercial CAD modeling environment. This facilitates a wide range of downstream technological applications. The modeled tool is used for finite element simulations to study the cutting flutes under static and transient dynamic load conditions. The results of stress distribution (von mises stress), translational displacement and deformation are presented for static and transient dynamic analysis for the end mill cutter flute and its body. The method described in this paper offers a simple and intuitive way of generating high-quality end mill models for use in machining process simulations. It can be easily extended to generate other tools without relying on analytical or numerical formulations.