Nonlinear Transient Dynamic Analysis Research Articles

Unit-cell-based derivation of the material models for armor-grade composites with different architectures of ultra-high molecular-weight polyethylene fibers

Purpose – Traditionally, an armor-grade composite is based on a two-dimensional (2D) architecture of its fiber reinforcements. However, various experimental investigations have shown that armor-grade composites based on 2D-reinforcement architectures tend to display inferior through-the-thickness mechanical properties, compromising their ballistic performance. To overcome this problem, armor-grade composites based on three-dimensional (3D) fiber-reinforcement architectures have recently been investigated experimentally. The paper aims to discuss these issues. Design/methodology/approach – In the present work, continuum-level material models are derived, parameterized and validated for armor-grade composite materials, having four (two 2D and two 3D) prototypical reinforcement architectures based on oriented ultra-high molecular-weight polyethylene fibers. To properly and accurately account for the effect of the reinforcement architecture, the appropriate unit cells (within which the constituent materials and their morphologies are represented explicitly) are constructed and subjected to a series of virtual mechanical tests (VMTs). The results obtained are used within a post-processing analysis to derive and parameterize the corresponding homogenized-material models. One of these models (specifically, the one for 0°/90° cross-collimated fiber architecture) was directly validated by comparing its predictions with the experimental counterparts. The other models are validated by examining their physical soundness and details of their predictions. Lastly, the models are integrated as user-material subroutines, and linked with a commercial finite-element package, in order to carry out a transient non-linear dynamics analysis of ballistic transverse impact of armor-grade composite-material panels with different reinforcement architectures. Findings – The results obtained clearly revealed the role the reinforcement architecture plays in the overall ballistic limit of the armor panel, as well as in its structural and damage/failure response. Originality/value – To the authors’ knowledge, the present work is the first reported attempt to assess, computationally, the utility and effectiveness of 3D fiber-reinforcement architectures for ballistic-impact applications.

Backbone curves with physical parameters for passive lateral response of homogeneous abutment backfills

Recent advances in performance-based seismic assessment and design of bridges call for the development of computationally efficient models with high fidelity for nonlinear static pushover and transient dynamic analyses. Response models of bridge abutment systems are significant ingredients of such analyses. Herein, we present closed-form relationships for lateral response of abutment backwalls with uniform backfills. These relationships are obtained by performing extensive parametric studies with a previously validated limit-equilibrium model coupled with hyperbolic soil stress–strain relations. The resulting “Generalized Hyperbolic Force–Displacement (GHFD)” backbone curve has explicit dependencies on the physical properties of the abutment system, including the backwall height. All input parameters to the GHFD relationships are measurable via standard geotechnical laboratory tests. We also perform a validation study using published measurements from several field and laboratory experiments. The GHFD equations are in closed form and can easily be implemented in a structural analysis package as a nonlinear spring that accounts for the bridge abutment–backfill interaction.

Derivation of the material models for ultra-high molecular-weight polyethylene fiber-reinforced armor-grade composites with different architectures

Purpose To overcome the problem of inferior through-the-thickness mechanical properties displayed by armor-grade composites based on 2-D reinforcement architectures, armor-grade composites based on 3D fiber-reinforcement architectures have recently been investigated experimentally. Design/methodology/approach The subject of the present work is armor-grade composite materials reinforced using ultra-high-molecular-weight polyethylene fibers and having four (two 2D and two 3D) prototypical architectures, as well as the derivation of the corresponding material models. The effect of the reinforcement architecture is accounted for by constructing the appropriate unit cells (within which the constituent materials and their morphologies are represented explicitly) and subjecting them to a series of virtual mechanical tests. The results obtained are used within a post-processing analysis to derive and parameterize the corresponding homogenized-material models. One of these models (specifically, the one for 0°/90° cross-collimated fiber architecture) was directly validated by comparing its predictions with the experimental counterparts. The other models are validated by examining their physical soundness and details of their predictions. Lastly, the models are integrated as user-material subroutines, and linked with a commercial finite-element package, in order to carry out a transient non-linear dynamics analysis of ballistic transverse impact of armor-grade composite-material panels with different reinforcement architectures. Findings It is found that the reinforcement architecture plays a critical role in the overall ballistic limit of the armor panel, as well as in its structural and damage/failure response. Originality/value To the authors’ knowledge, the present work is the first reported attempt to assess, computationally, the utility and effectiveness of 3D fiber-reinforcement architectures for ballistic impact applications.

Ballistic Impact Behavior of Nacre-Like Laminated Composites Consisting of B4C Tablets and Polyurea Matrix

A nacre-like composite armor consisting of B4C tablets and polyurea matrix is modeled, and its ballistic impact behavior and penetration resistance (under a normal and a 15°-oblique impact by a solid right circular cylindrical projectile) were analyzed using a series of transient, nonlinear dynamic, finite-element analyses. Nacre is a biological material constituting the innermost layer of the shells of gastropods and bivalves. It consists of polygonal tablets of aragonite, tessellated to form individual layers and having the adjacent layers as well as the tablets within a layer bonded by a biopolymer. Due to its highly complex hierarchical microstructure, nacre possesses an outstanding combination of mechanical properties, the properties which are far superior to the ones that are predicted using the homogenization techniques such as the rule of mixtures. The results of the transient nonlinear dynamic analysis pertaining to the ballistic impact response and the penetration resistance of the modeled nacre-like armor are compared with their counterparts for the B4C single-block armor having an identical areal density. Furthermore, the effect of various nacre microstructural features (e.g., surface profiling, micron-scale asperities, mineral bridges between the overlapping tablets lying in adjacent layers) on the ballistic penetration resistance of the nacre-like composite armor is investigated in order to identify an optimal nacre-like composite-armor architecture having the largest penetration resistance. The results obtained clearly show that a nacre-like armor possesses a superior penetration resistance relative to its monolithic counterpart, and that the nacre microstructural features considered play a critical role in the armor penetration resistance.

Non-linear transient dynamic analysis of sandwich plate with composite face-sheets embedded with shape memory alloy wires and flexible core- based on the mixed LW (layer-wise)/ESL (equivalent single layer) models

In this study, a nonlinear dynamic analysis of sandwich plate with flexible core and laminated composite face sheets embedded with shape memory alloy (SMA) wires is investigated using the mixed LW/ESL models in the framework of Carrera's Unified Formulation. The instantaneous phase transformation effects are considered for every point on the face sheets. Since, this research deals with the transient nonlinear problem and the structure is thick plate with flexible core, employing a model with high accuracy and low computational cost is vital in this work. For this aim, the new mixed LW/ESL models proposed are employed in this study. The constitutive equation proposed by Brinson is used for modeling the nonlinear behavior of SMA wires. The governing equations are derived employing the Reissner Mixed Variational Theorem (RMVT) in order to satisfy the interlaminar continuity of transverse stresses between the layers. The nonlinear governing equations are solved based on the transient finite element along with the iterative incremental method. Some parametric studies such as intensity of impulsive pressure, location of SMA wires, plate aspect ratio, ratio of face sheet's thickness to the total thickness, volume fraction of the SMA wires and also boundary conditions upon the loss factor are investigated.

Three-Dimensional Dynamic Model of TEHD Tilting-Pad Journal Bearing—Part II: Parametric Studies

This paper presents a new analysis method for a thermo-elasto-hydro-dynamic (TEHD) tilting pad journal bearing (TPJB) system to reach a static equilibrium condition adopting nonlinear transient dynamic solver, whereas earlier studies have used iteration schemes such as Newton–Raphson method. The theoretical TPJB model discussed in Part I of this research is combined into a newly developed algorithm to perform a bearing dynamic analysis and present dynamic coefficients. In the nonlinear transient dynamic solver, physical and modal coordinates coexist for computational efficiency, and transformation between modal and physical coordinate is performed at each numerical integration time step. Variable time step Runge–Kutta numerical integration scheme is adopted for a reliable and fast calculation. Nonlinear time transient dynamic analysis and steady thermal analysis are combined to find the static equilibrium condition of the TPJB system, where the singular matrix issue of flexible pad finite element (FE) model is resolved. The flexible pad TPJB model was verified by comparison with other numerical results. Simulation results corresponding with the theoretical model explained in Part I are presented and discussed. It explains how the TPJB dynamic behavior is influenced by a number of eigenvector of flexible pad FE model and pad thickness. Preload change under fluid and thermal load is examined.

Nonlinear Dynamic Analysis of High Speed Oil-Free Turbomachinery With Focus on Stability and Self-Excited Vibration

This paper presents a generic technique for the transient nonlinear dynamic analysis (TNDA) and the static equilibrium stability analysis (SESA) of a turbomachine running on foil air bearings (FABs). This technique is novel in two aspects: (i) the turbomachine structural model is generic, based on uncoupled modes (rotor is flexible, nonsymmetric and includes gyroscopic effects; dynamics of support structure can be accommodated) and (ii) the finite-difference (FD) state equations of the air films are preserved and solved simultaneously with the state equations of the foil structures and the state equations of the turbomachine modal model, using a readily available implicit integrator (for TNDA) and a predictor-corrector approach (for SESA). An efficient analysis is possible through the extraction of the state Jacobian matrix using symbolic computing. The analysis is first applied to the finite-element model of a small commercial automotive turbocharger that currently runs on floating ring bearings (FRBs) and is slightly adapted here for FABs. The results of SESA are shown to be consistent with TNDA. The case study shows that, for certain bearing parameters, it is possible to obtain a wide speed range of stable static equilibrium operation with FABs, in contrast to the present installation with FRBs. Application of the method to a test rig reported in the literature reveals a reasonable degree of correlation between theory and experiment.

Seismic vulnerability assessment of a RC structure before and after FRP retrofitting

In earthquake engineering, reliable vulnerability assessment tools suitable to existing reinforced concrete structures are necessary in order to mitigate the seismic risk. Furthermore, amongst the wide range of technical solutions available for structural upgrading, external reinforcement by fiber reinforced polymer (FRP) is often an interesting option. Nevertheless, the use of FRP is limited, one of the reasons being the lack of predictive numerical tools allowing for vulnerability assessment. Based on a case study, this article presents a simplified modeling strategy to assess the seismic vulnerability of an existing reinforced concrete building before and after FRP retrofitting. The structure is simulated using multifiber beam elements and constitutive laws based on damage mechanics and plasticity, while the dynamic characteristics of the numerical model are validated using in-situ ambient vibration records. Nonlinear transient dynamic analysis studies are performed using a synthetic earthquake signal compatible with the Eurocode 8 spectra. Local indicators are adopted to quantify the damage level in the structure before and after FRP retrofitting, in correspondence with the European Macroseismic Scale 98. One of the main conclusions of this study is that the use of local indicators can lead to contradictory assessment results with the evaluations based on global indicators as adopted in HAZUS or Risk-UE.

Three-Dimensional Thermohydrodynamic Morton Effect Simulation—Part I: Theoretical Model

The present study is focused on accurate prediction of the Morton effect problem including journal asymmetric heating and the corresponding long period amplitude oscillations using a nonlinear time transient rotor-dynamic simulation. This paper presents a theoretical model of thermal induced synchronous instability problems in a nonlinear rotor–bearing system, and suggests a new computational algorithm for the nonlinear transient analysis of the Morton effect where the dynamic and thermal problems are combined. For the analysis of the Morton effect problem, a variable viscosity Reynolds equation and a 3D energy equation are coupled via temperature and viscosity, and solved simultaneously. Three-dimensional heat transfer equations of bearing and shaft are modeled by a finite element method, and thermally coupled with the fluid film via a heat flux boundary condition. Asymmetric heat flux into the synchronously whirling rotor is solved by the orbit time averaged heat flux from fluid film to the spinning shaft surface. The journal orbit is calculated by the nonlinear transient dynamic analysis of a rotor–bearing system with a variable time step numerical integration scheme. For the computation time reduction, modal coordinate transformation is adopted in dynamic and thermal transient analysis. Thermal bow effect makes a significant change to the dynamic behavior of a rotor–bearing system, and a thermal hysteresis bode plot, that is one of the characteristics of the Morton effect problem, is presented with time varying spin speed.

Disturbance Sampling Analysis in Sediment of the Yellow River Reservoir by Finite Element Method

Based on the nonlinear finite element theory, the disturbance conditions of deep water reservoir sediment in the process of sampling with sampler are researched by using the finite element software ADINA. Nonlinear face-face contact model between sampler and sediment is established by adopting the Mohr-Coulomb constitutive model as sediments material properties, and the friction and contact in the interface of sampler wall and sediment are well simulated. The impact load is applied, and the impact sampling finite element simulation model is obtained by nonlinear transient dynamic analysis. The condition of deformation, stress and strain in sampling sampler is well discussed, the results show that the axial compression of sediment samples is largest on the bit lip surface and is smallest in the center part of the sediment samples, the impact disturbance on the soil samples is within a small scope nearby the bits.

Vibrations of an aramid anchor cable subjected to turbulent wind

The vibration response of an initially pre-stressed anchor cable made of parallel-lay aramid fibres excited by a measured and artificially simulated spatial turbulent wind field is presented in the paper. Results of the analyses of in situ measured wind records are described. For selected data set statistical characteristics and power spectral density functions of the measured wind velocity components are calculated. The wind stochastic velocity fluctuation is modelled as a one-variate bi-dimensional random field. Cross-power spectral density functions, at different point locations are introduced. The combination of the weighted amplitude wave superposition method (WAWS) with the Shinozuka–Deodatis method is used for the analyzed problem. A time-dependent behaviour of the synthetic cable is investigated which is subjected to turbulent wind with large expected oscillations that arise as a result of slackening due to the relaxation effects. A nonlinear transient dynamic analysis is used in conjunction with the finite element method to determine the dynamic response of the cable subjected to turbulent wind at its initially prestressed state and in the selected times after the relaxation effect. The constitutive equation of the relaxation of the aramid cable follows an experimentally obtained law of the logarithmic type. To monitor the dependences of the individual quantities of cable vibration in the phase space, attractors and Poincaré maps are created by sampling the cable’s displacement and velocity at periods of relevant frequencies. Interesting findings based on the response of the cable with rheological properties to turbulent wind are presented.

Crashworthiness optimisation of vehicle structures with magnesium alloy parts

This paper explores the effects of replacing the baseline steel with lightweight magnesium alloy parts on crashworthiness characteristics and optimum design of a full-vehicle model. Full frontal, offset frontal and side crash simulations are performed on a validated 1996 Dodge Neon model using explicit nonlinear transient dynamic finite element analyses in LS-DYNA to obtain vehicle responses such as crash pulse, intrusion distance, peak acceleration and internal energy. Twenty-two parts of the vehicle body structure are converted into AZ31 magnesium alloy with adjustable wall thickness while the remaining parts are kept intact. The magnesium alloy material model follows a piecewise linear plasticity law considering separate tension and compression properties and maximum plastic strain failure criterion. Six different metamodelling techniques including optimised ensemble are developed and tuned for predictions of crash-induced responses within the design optimisation process. The crashworthiness optimisation problem is solved using the sequential quadratic programming method with most accurate surrogate models of structural responses considering both constrained single- and multi-objective formulations. The results show that under the combined crash scenarios with the selected material models and design constraints, the vehicle model with magnesium alloy parts can be optimised to maintain or improve its crashworthiness characteristics with up to 50% weight savings in the redesigned parts.

Experimental and Numerical Study for the Shear Strengthening of Reinforced Concrete Beams Using Textile-Reinforced Mortar

In this paper, the effectiveness of textile-reinforced mortars (TRMs), as a means of increasing the shear resistance of reinforced concrete beams, is experimentally and numerically investigated. Textiles comprise of fabric meshes made of long woven, knitted or even unwoven fiber rovings in at least two (typically orthogonal) directions. Mortars—serving as binders—may (or may not) contain polymeric additives usually used to have improved strength properties. These TRMs may be considered as an alternative to fiber-reinforced polymers (FRP), providing solutions to many of the problems associated with application of the latter without compromising much of the performance of strengthened members. In the present study, a new type of textile (basalt-based textile) was used as strengthening material. Two different mortar types’ viz. cementitious and polymer-modified cementitious mortars were used as binding material for the textile sheets. The studied parameters also included the number of textile layers as well as the orientation of the textile material. The experimental program comprises of testing two control beams which were intentionally designed to be deficient in shear, in addition to testing eight beams which were externally upgraded by TRM sheets for enhancing their shear capacity. On the basis of the experimental response of reinforced concrete members strengthened in shear, it is concluded that textile-mortar composite provides substantial gain in shear resistance; this gain is higher as the number of layers increases. With higher number of layers, textile with 45° orientation along with polymer-modified cementitious mortar provides the highest shear strength enhancement. Nonlinear finite-element (FE) analysis was also carried out on the tested beams using LS-DYNA, which is transient nonlinear dynamic analysis software. The numerical analysis carried out involved case studies for TRM modeled, with and without mortar. Good agreement was achieved between the experimental and numerical results especially for the ultimate load carrying capacity for the case of FE models incorporating mortar. The study was extended numerically to include additional cases of TRM-strengthened specimens with more number of TRM layers as well as a case of FRP-strengthened specimen.

Dynamic buckling of a laminated composite stringer–stiffened cylindrical panel

The present study deals with the “dynamic buckling” of a laminated composite stringer–stiffened curved panel. The “dynamic buckling”, in the present study, is concerned with the unbounded lateral response of the panel, which is subjected to an axial impact load.In reinforced panels with widely spaced adequately stiff stringers, the structure may pass through two major states before its total collapse: buckling of the panel skin between stiffeners and buckling of the stiffeners themselves. This study focuses on the lowest buckling load of the stringer–stiffened panel, which is, buckling of the panel skin between stiffeners.The analysis of the laminated composite stringer–stiffened cylindrical panel was performed by using the commercial ANSYS finite element software. The model simulates the structure and its associated boundary conditions. The boundary conditions simulate the stringer–stiffened cylindrical panel as a part of a fuselage. The static buckling analysis was performed using the eigenvalue buckling approach to determine the static critical load. Modal analysis was used to calculate the first natural frequency and corresponding mode shape of the structure. Nonlinear transient dynamic analysis was used to determine the dynamic critical load. In the transient dynamic analysis the Newmark method with the Newton–Raphson scheme were used.In the present study, the equation of motion approach was applied. By this approach, the equations of motion were numerically solved for various load parameter values (loading amplitude and loading duration) to obtain the system response. Special attention was given to the neighborhood of loading durations corresponding to the period of the lowest bending frequency of the skin.For each load duration, the dynamic buckling load was calculated using a load versus lateral displacement curve generated by the ANSYS code.The results were plotted on a dynamic load amplification factor (DLF) graph. The DLF is defined, as the ratio of the dynamic buckling to the static buckling of the panel. For loading periods in the neighborhood of the lowest natural frequency of the panel, the DLF was less than unity. It means that, for those particular loading periods, the dynamic buckling load is lower than the static one.

Numerical prediction of dynamic response of RC beams

In this study, an attempt has been made to develop a finite-element numerical procedure for the non-linear transient dynamic analysis of reinforced concrete (RC) beams. New material constitutive relationships have been employed depending on various experimental data. Eight-node serendipity degenerated plate elements have been used to represent the concrete beam elements. A layered approach was adopted to discretise the concrete and steel reinforcement through the thickness of the beam. Strain-hardening plasticity and elastic perfectly plastic models have been used to model the compressive behaviour of the concrete used in this study. Strain rate effect was included by assuming the dynamic yield function to be a function of the current strain rate in addition to being the total plastic strain. Geometrical non-linearity in the layered approach is considered in the mathematical model, which is based on the total Lagrangian approach taking into account Von Karman assumptions. A new model is used to consider the effect of tension stiffening in the cracked concrete. Steel reinforcement is considered as an elastic plastic material with linear strain hardening. Implicit Newmark with a corrector–predictor algorithm is employed for time integration of the equation of the motion. A computer program coded in MATLAB has been developed for the non-linear finite-element dynamic analysis of RC beams subjected to the dynamic loadings. Finally, various numerical examples validating the proposed formulation are given.

Investigation on the Effects of Depth-to-Span Ratio of Tensegrity Flat Grids on Their Seismic Behavior

Tensegrity state is a stable self-equilibrated state of a spatial system that contains a non-continuous set of compressive elements (struts) inside a continuous set of self-tensioned elements (cables). At the present study, the seismic behavior of double layer flat tensegrity grids consisted of quadrangular tensegrity prisms, have been investigated by carrying out nonlinear full transient time-history dynamic analysis. In order to determine the effects of depth-to-span ratio on seismic behavior of flat tensegrity grids, several non-linear time history analyses have been performed by ANSYS finite element program. Three 1/10, 1/12 & 1/15 grid depth-to-span ratios have been considered for investigation. Then the effects of depth-to-span ratio on seismic behavior of tensegrity flat grids have been determined. It is shown that these systems are sensitive and vulnerable against seismic excitations. Based on the obtained results, some design recommendations have been presented regarding to the seismic behavior of these systems.

Structural design optimization of racing motor boat based on nonlinear finite element analysis

Since 1980's, optimum design techniques for ship structural design have been developed to the preliminary design which aims at minimum weight or minimum cost design of mid-ship section based on analytic structural analysis. But the optimum structural design researches about the application for the detail design of local structure based on FEA have been still insufficient. This paper presents optimization technique for the detail design of a racing motor boat. To improve the performance and reduce the damage of a real existing racing boat, direct structural analyses; static and non-linear transient dynamic analyses, were carried out to check the constraints of minimum weight design. As a result, it is shown that the optimum structural design of a racing boat has to be focused on reducing impulse response from pitching motion than static response because the dynamic effect is more dominant. Optimum design algorithm based on nonlinear finite element analysis for a racing motor boat was developed and coded to ANSYS, and its applicability for actual structural design was verifed.

Bird strike damage analysis in aircraft structures using Abaqus/Explicit and coupled Eulerian Lagrangian approach

The subject of this paper is numerical prediction of bird strike induced damage in real aeronautical structures using highly detailed finite element models and modern numerical approaches. Due to the complexity of today’s aeronautical structures, numerical damage prediction methods have to be able to take into account various failure and degradation models of different materials. A continuum damage mechanics approach has been employed to simulate failure initiation and damage evolution in unidirectional composite laminates. Hashin’s failure initiation criteria have been employed in order to be able to distinct between four ply failure modes. The problem of soft body impacts has been tackled by applying the Coupled Eulerian Lagrangian technique, thereby avoiding numerical difficulties associated with extensive mesh distortion. This improvement in impactor deformation modelling resulted in a more realistic behaviour of bird material during impact. Numerical geometrical and material nonlinear transient dynamic analyses have been performed using Abaqus/Explicit. The main focus of the work presented in this paper is the application of the damage prediction procedure in damage assessment of bird impact on a typical large airliner inboard flap structure. Due to the high cost of gas-gun testing of aircraft components, experimental testing on the real flap structure could not have been performed. In order to evaluate the accuracy of the presented method, the bird and composite damage model have been validated against experimental data available in the literature.

Experimental Evaluation of Pretopped Precast Diaphragm Critical Flexure Joint under Seismic Demands

Precast concrete diaphragm seismic response is examined in experimental research integrating model-based simulation with physical testing. The experimental substructure is the diaphragm critical flexural region of a prototype precast parking structure. This region is expected to undergo significant inelastic flexural deformation, while potentially nonductile regions remain elastic on the basis of capacity design rules from an emerging design methodology. The physical test is conducted at half-scale. The test specimen is detailed using diaphragm reinforcement intended to meet deformability requirements. Predetermined displacement histories are applied to the test specimen on the basis of nonlinear transient dynamic analyses of the prototype structure. The loading history is applied by a test fixture capable of simultaneously providing shear, axial, and moment to the joint. Moment strength, stiffness, rotational deformation capacity, and progressive damage are examined under a sequence of increasing intensity earthquakes. Design recommendations are provided.

Structural design optimization of racing motor boat based on nonlinear finite element analysis

Since 1980's, optimum design techniques for ship structural design have been developed to the preliminary design which aims at minimum weight or minimum cost design of mid-ship section based on analytic structural analysis. But the optimum structural design researches about the application for the detail design of local structure based on FEA have been still insufficient. This paper presents optimization technique for the detail design of a racing motor boat. To improve the performance and reduce the damage of a real existing racing boat, direct structural analyses; static and non-linear transient dynamic analyses, were carried out to check the constraints of minimum weight design. As a result, it is shown that the optimum structural design of a racing boat has to be focused on reducing impulse response from pitching motion than static response because the dynamic effect is more dominant. Optimum design algorithm based on nonlinear finite element analysis for a racing motor boat was developed and coded to ANSYS, and its applicability for actual structural design was verifed.