Search results for: geometric nonlinearity

Authors: Shun-Qi Zhang, Shu-Yang Zhang, Min Chen, , Jing Bai

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Piezoelectric laminated smart structures can be subjected to the strong driving electric field, which may result in large displacements and rotations. In one hand, piezoelectric materials usually behave very significant material nonlinear effects under strong electric fields. On the other hand, thin-walled structures undergoing large displacements and rotations exist nonnegligible geometric nonlinearity. In order to give a precise prediction of piezo laminated smart structures under the large electric field, this paper develops a finite element (FE) model accounting for material nonlinearity (piezoelectric part) and geometric nonlinearity based on the first order shear deformation (FSOD) hypothesis. The proposed FE model is first validated by both experimental and numerical examples from the literature. Afterwards, it is applied to simulate for plate and shell structures with multiple piezoelectric patches under the strong applied electric field. From the simulation results, it shows that large discrepancies occur between linear and nonlinear predictions for piezoelectric laminated structures driving at the strong electric field. Therefore, both material and geometric nonlinearities should be taken into account for piezoelectric structures under strong electric.

Keywords: piezoelectric smart structures, finite element analysis, geometric nonlinearity, electroelastic material nonlinearities

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Authors: M. Seguini, D. Nedjar

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An accuracy nonlinear analysis of a deep beam resting on elastic perfectly plastic soil is carried out in this study. In fact, a nonlinear finite element modeling for large deflection and moderate rotation of Euler-Bernoulli beam resting on linear and nonlinear random soil is investigated. The geometric nonlinear analysis of the beam is based on the theory of von Kàrmàn, where the Newton-Raphson incremental iteration method is implemented in a Matlab code to solve the nonlinear equation of the soil-beam interaction system. However, two analyses (deterministic and probabilistic) are proposed to verify the accuracy and the efficiency of the proposed model where the theory of the local average based on the Monte Carlo approach is used to analyze the effect of the spatial variability of the soil properties on the nonlinear beam response. The effect of six main parameters are investigated: the external load, the length of a beam, the coefficient of subgrade reaction of the soil, the Young’s modulus of the beam, the coefficient of variation and the correlation length of the soil’s coefficient of subgrade reaction. A comparison between the beam resting on linear and nonlinear soil models is presented for different beam’s length and external load. Numerical results have been obtained for the combination of the geometric nonlinearity of beam and material nonlinearity of random soil. This comparison highlighted the need of including the material nonlinearity and spatial variability of the soil in the geometric nonlinear analysis, when the beam undergoes large deflections.

Keywords: finite element method, geometric nonlinearity, material nonlinearity, soil-structure interaction, spatial variability

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Authors: Shun-Qi Zhang, Shu-Yang Zhang, Min Chen

Abstract:

Applying strong electric field on piezoelectric actuators, on one hand very significant electroelastic material nonlinear effects will occur, on the other hand piezo plates and shells may undergo large displacements and rotations. In order to give a precise prediction of piezolaminated smart structures under large electric field, this paper develops a finite element (FE) model accounting for both electroelastic material nonlinearity and geometric nonlinearity with large rotations based on the first order shear deformation (FSOD) hypothesis. The proposed FE model is applied to analyze a piezolaminated semicircular shell structure.

Keywords: smart structures, piezolamintes, material nonlinearity, strong electric field

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Authors: Gyu-Jin Kim, Hyo-Gyoung Kwak

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In this research, the effect of prestressing force on the nonlinearity of concrete was investigated by an experimental study. For the measurement of ultrasonic nonlinearity, a prestressed concrete beam was prepared and a nonlinear resonant ultrasound method was adopted. When the prestressing force changes, the stress state of the concrete inside the beam is affected, which leads to the occurrence of micro-cracks and changes in mechanical properties. Therefore, it is necessary to introduce nonlinear ultrasonic technology which sensitively reflects microstructural changes. Repetitive prestressing load history, including maximum levels of 45%, 60% and 75%, depending on the compressive strength, is designed to evaluate the impact of loading levels on the nonlinearity. With the experimental results, the possibility of ultrasonic nonlinearity as a trial indicator of stress was evaluated.

Keywords: micro crack, nonlinear ultrasonic resonant spectroscopy, prestressed concrete beam, prestressing force, ultrasonic nonlinearity

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Authors: Ruichong Zhang

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This study proposes a recording-based approach to characterize and quantify earthquake-induced site nonlinearity, exemplified as soil nonlinearity and/or liquefaction. Alternative to Fourier spectral analysis (FSA), the paper introduces time-frequency analysis of earthquake ground motion recordings with the aid of so-called Hilbert-Huang transform (HHT), and offers justification for the HHT in addressing the nonlinear features shown in the recordings. With the use of the 2001 Nisqually earthquake recordings, this study shows that the proposed approach is effective in characterizing site nonlinearity and quantifying the influences in seismic ground responses.

Keywords: site nonlinearity, site amplification, site damping, Hilbert-Huang Transform (HHT), liquefaction, 2001 Nisqually Earthquake

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Authors: Hasan Çiçekli, Ahmet Gökçen, Uğur Çam

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In this paper, a comparative performance analysis of mostly used four nonlinearity cancellation techniques used to realize the passive resistor by MOS transistors is presented. The comparison is done by using an integrator circuit which is employing sequentially Op-amp, OTRA and ICCII as active element. All of the circuits are implemented by MOS-C realization and simulated by PSPICE program using 0.35 µm process TSMC MOSIS model parameters. With MOS-C realization, the circuits became electronically tunable and fully integrable which is very important in IC design. The output waveforms, frequency responses, THD analysis results and features of the nonlinearity cancellation techniques are also given.

Keywords: integrator circuits, MOS-C realization, nonlinearity cancellation, tuneable resistors

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Authors: G. Akgun, I. Algul, H. Kurtaran

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In this paper geometrically nonlinear static behavior of laminated composite hollow super-elliptic beams is investigated using generalized differential quadrature method. Super-elliptic beam can have both oval and elliptic cross-sections by adjusting parameters in super-ellipse formulation (also known as Lamé curves). Equilibrium equations of super-elliptic beam are obtained using the virtual work principle. Geometric nonlinearity is taken into account using von-Kármán nonlinear strain-displacement relations. Spatial derivatives in strains are expressed with the generalized differential quadrature method. Transverse shear effect is considered through the first-order shear deformation theory. Static equilibrium equations are solved using Newton-Raphson method. Several composite super-elliptic beam problems are solved with the proposed method. Effects of layer orientations of composite material, boundary conditions, ovality and ellipticity on bending behavior are investigated.

Keywords: generalized differential quadrature, geometric nonlinearity, laminated composite, super-elliptic cross-section

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Authors: Khelil Khadidja

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In this paper, blackness of dark solitons is considered. The exact combination between nonlinearity and dispersion is responsible of solitons stability. Dark solitons get born when dispersion is abnormal and balanced by nonlinearity, at the opposite of brillant solitons which is born by normal dispersion and nonlinearity together. Thanks to their stability, dark solitons are suitable for transmission by optical fibers. Dark solitons which are a solution of Nonlinear Schrodinger equation are simulated with Matlab to discuss the influence of coefficient of blackness. Results show that there is a direct proportion between the coefficient of blackness and the intensity of dark soliton. Those gray solitons are stable and convenient for transmission.

Keywords: abnormal dispersion, nonlinearity, optical fiber, soliton

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Authors: Moumita Sit, Chaitali Ray

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The present article deals with the free vibration analysis of hybrid laminated composite structures with initial stresses developed in the laminates. Generally initial stresses may be developed in the laminates by temperature and moisture effect. In this study, an eight noded isoparametric plate bending element has been used for the finite element analysis of composite plates. A numerical model has been developed to assess the geometric nonlinear response of composite plates based on higher order shear deformation theory (HSDT) considering the Green–Lagrange type nonlinearity. A computer code based on finite element method (FEM) has also been developed in MATLAB to perform the numerical calculations. To validate the accuracy of the proposed numerical model, the results obtained from the present study are compared with those available in published literature. Effects of the side to thickness ratio, different boundary conditions and initial stresses on the natural frequency of composite plates have been studied. The free vibration analysis of a hollow stiffened hybrid laminated panel has also been carried out considering initial stresses and presented as case study.

Keywords: geometric nonlinearity, higher order shear deformation theory (HSDT), hybrid composite laminate, the initial stress

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Authors: Ridzuan Hussin, Mohd Zaihidee Arshad

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The creativity of earlier artists and sculptors in designing geometric is extraordinary provided with only a compass. Indeed, geometric in Islamic art and design are unique and have their own aesthetic values. In order to further understand geometric, self-learning with the approach of hands on would be appropriate. For this study, Islamic themed geometric designed and created, concerning only; i. The Square Repetition Unit and √2, ii. The Hexagonal Repetition Unit and √3 and iii. Double Hexagon. The aim of this research is to evaluate the creativity of Islamic geometric pattern artworks, through Fundamental Arts and Gestalt theory. Data was collected using specific tasks, and this research intends to identify the difference of Islamic geometric between 21 untitled selected geometric artworks (conventional design method), and 25 digital untitled geometric pattern artworks method. The evaluation of creativity, colors, layout, pattern and unity is known to be of utmost importance, although there are differences in the conventional or the digital approach.

Keywords: Islamic geometric design, Gestalt, fundamentals of art, patterns

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Authors: Keyvan Ramin

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The geometric nonlinearity of Off-Diagonal Bracing System (ODBS) could be a complementary system to covering and extending the nonlinearity of reinforced concrete material. Finite element modeling is performed for flexural frame, x-braced frame and the ODBS braced frame system at the initial phase. Then the different models are investigated along various analyses. According to the experimental results of flexural and x-braced frame, the verification is done. Analytical assessments are performed in according to three-dimensional finite element modeling. Non-linear static analysis is considered to obtain performance level and seismic behavior, and then the response modification factors calculated from each model’s pushover curve. In the next phase, the evaluation of cracks observed in the finite element models, especially for RC members of all three systems is performed. The finite element assessment is performed on engendered cracks in ODBS braced frame for various time steps. The nonlinear dynamic time history analysis accomplished in different stories models for three records of Elcentro, Naghan, and Tabas earthquake accelerograms. Dynamic analysis is performed after scaling accelerogram on each type of flexural frame, x-braced frame and ODBS braced frame one by one. The base-point on RC frame is considered to investigate proportional displacement under each record. Hysteresis curves are assessed along continuing this study. The equivalent viscous damping for ODBS system is estimated in according to references. Results in each section show the ODBS system has an acceptable seismic behavior and their conclusions have been converged when the ODBS system is utilized in reinforced concrete frame.

Keywords: FEM, seismic behaviour, pushover analysis, geometric nonlinearity, time history analysis, equivalent viscous damping, passive control, crack investigation, hysteresis curve

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Authors: N. Manoj

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The aeroelastic behavior of engine nacelle strake when subjected to unsteady aerodynamic flows is investigated in this paper. Geometric nonlinear characteristics and modal parameters of nacelle strake are studied when it is under dynamic loading condition. Here, an N-S based Finite Volume solver is coupled with Finite Element (FE) based nonlinear structural solver to investigate the nonlinear characteristics of nacelle strake over a range of dynamic pressures at various phases of flight like takeoff, climb, and cruise conditions. The combination of high fidelity models for both aerodynamics and structural dynamics is used to predict the nonlinearities of strake (chine). The methodology adopted for present aeroelastic analysis is partitioned-based time domain coupled CFD and CSD solvers and it is validated by the consideration of experimental and numerical comparison of aeroelastic data for a cropped delta wing model which has a proven record. The present strake geometry is derived from theoretical formulation. The amplitude and frequency obtained from the coupled solver at various dynamic pressures is discussed, which gives a better understanding of its impact on aerodynamic design-sizing of strake.

Keywords: aeroelasticity, finite volume, geometric nonlinearity, limit cycle oscillations, strake

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Authors: Morteza Shayan Arani, Mohammadamin Esmailzadehazimi, Mohammadreza Moeini, Mohammad Toorani, Aouni A. Lakis

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This paper investigates the nonlinear response of thin, incompressible, hyperelastic cylindrical shells in the presence of a time-varying temperature field while considering initial geometric imperfections. The governing equations of motion are derived using an improved Donnell's shallow shell theory. The hyperelastic material is modeled using the Mooney-Rivlin model with two parameters, incorporating temperature-dependent terms. The Lagrangian method is applied to obtain the equation of motion. The resulting governing equation is addressed through the Lindstedt-Poincaré and Multiple Scale methods. The linear and nonlinear models presented in this study are verified against existing open literature, demonstrating the accuracy and reliability of the presented model. The study focuses on understanding the influence of temperature variations and geometrical imperfections on the natural frequency and amplitude-frequency response of the systems. Notably, the investigation reveals the coexistence of hardening and softening peaks in the amplitude-frequency response, which vary in magnitude depending on these parameters. Additionally, resonance peaks exhibit changes as a result of temperature and geometric imperfections.

Keywords: hyperelastic material, cylindrical shell, geometrical nonlinearity, material naolinearity, initial geometric imperfection, temperature gradient, hardening and softening

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Authors: Ferdağ Çulhan, Emine Gaye Çontay

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Geometric thinking levels created by Van Hiele are used to determine students' progress in geometric thinking. Many studies have been conducted on geometric thinking levels and they have taken their place in teaching curricula over time. It is thought that geometric thinking levels, which have become so important in teaching, can be examined in depth. In order to make an in-depth analysis, it was decided that the most appropriate management was discourse analysis. In this study, the focus is on examining the geometric thinking levels of 8th grade students from a discursive point of view. Sfard (2008)'s "Commognitive" theory will be used to conduct discursive analysis. The "Global Van Hiele Questionnaire" created by Patkin (2014) and translated into Turkish for this research will be used in the research. The "Global Van Hiele Questionnaire" contains questions from the sub-learning domain of triangles and quadrilaterals, circles and geometric objects. It has a wider scope than many "Van Hiele Questionnaires". “Global Van Hiele Questionnaire” will be applied to 8th grade students. Then, the geometric thinking levels of the students will be determined and interviews will be held with two students from each of the 1st, 2nd and 3rd levels. The interviews will be recorded and the students' discourses will be examined. By evaluating the relations between the students' geometric thinking levels and their discourses, it will be examined how much their discourse reflects their level of thinking. In this way, it is thought that students' geometric thinking processes can be better understood.

Keywords: mathematical discourses, commognitive framework, geometric thinking levels, van hiele

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Authors: Shu-Yang Zhang, Shun-Qi Zhang, Zhan-Xi Wang, Xian-Sheng Qin

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Thin-walled structures are used more and more widely in modern aircrafts and some other structures in aerospace field nowadays. Accompanied by the wider applications, the vibration of the structures has been a bigger problem. Because of the direct and converse piezoelectric effect, piezoelectric materials combined to host thin-walled structures, named as piezoelectric smart structures, can be an effective way to suppress the vibration. So, an accurate model for piezoelectric thin-walled structures in air flow is necessary and important. In our recent work, an electromechanical coupling nonlinear aerodynamic finite element model of piezoelectric smart thin-walled structures is built based on the Reissner-Mindlin plate theory and first-order piston theory for aerodynamic pressure of supersonic flow. Von Kármán type nonlinearity is considered in the present model. Finally, the model is validated by experimental and numerical results from the literature, which can describe the vibration of the structures in supersonic flow precisely.

Keywords: piezoelectric smart structures, aerodynamic, geometric nonlinearity, finite element analysis

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Authors: Abdullah Eqal Al Mazrooei

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In this paper, a nonlinear dynamical system is presented. This system is a bilinear class. The bilinear systems are very important kind of nonlinear systems because they have many applications in real life. They are used in biology, chemistry, manufacturing, engineering, and economics where linear models are ineffective or inadequate. They have also been recently used to analyze and forecast weather conditions. Bilinear systems have three advantages: First, they define many problems which have a great applied importance. Second, they give us approximations to nonlinear systems. Thirdly, they have a rich geometric and algebraic structures, which promises to be a fruitful field of research for scientists and applications. The type of nonlinearity that is treated and analyzed consists of bilinear interaction between the states vectors and the system input. By using some properties of the tensor product, these systems can be transformed to linear systems. But, here we discuss the nonlinearity when the state vector is multiplied by itself. So, this model will be able to handle evolutions according to the Lotka-Volterra models or the Lorenz weather models, thus enabling a wider and more flexible application of such models. Here we apply by using an estimator to estimate temperatures. The results prove the efficiency of the proposed system.

Keywords: Lorenz models, nonlinear systems, nonlinear estimator, state-space model

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Authors: Edamana Vasudevan Krishnan

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This paper studies solitons in optical materials with the help of Mapping Method. Two types of nonlinear media have been investigated, namely, the cubic nonlinearity and the quintic nonlinearity. The soliton solutions, shock wave solutions and singular solutions have been derives with certain constraint conditions.

Keywords: solitons, integrability, metamaterials, mapping method

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Authors: Chia-Hung Liao, Shih-Chieh Lin

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X-ray computed tomography (CT) technology has been used in the electronics industry as one of the non-destructive inspection tools for years. The key advantage of X-ray computed tomography technology superior to traditional optical inspection is the penetrating characteristics of X-rays can be used to detect defects in the interior of objects. The objective of this study is to find a way to estimate the system geometric deviation of X-ray CT equipment. Projection trajectories of the characteristic points of standard parts were tracked, and ways to calculate the deviation of various geometric parameters of the system will be proposed and evaluated. A simulation study will be conducted to first find out the effects of system geometric deviation on projected trajectories. Then ways to estimate geometric deviation with collected trajectories will be proposed and tested through simulations.

Keywords: geometric calibration, X-ray computed tomography, trajectory tracing, reconstruction optimization

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Authors: Nima Valibeig, Haniyeh Mohammadi, Neda Sadat Abdelahi

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Persian domes follow different forms depending on the materials used to construct and other factors. One of the factors that shape the form of a dome is the geometric proportion used in the drawing and construction of the dome. Some commonly used proportions are revealed by analysing the shapes and geometric ratio of the monuments’ domes. The proportions are achieved by the proficiency of the skilled architects of the buildings. These proportions can be used to reconstruct damaged parts of the historical monuments. Most of the research on domes is about the historical or stability features of domes, and less attention is made to the geometric system in domes. Therefore, in this study, we study the explicit and implicit geometric proportions in Iranian dome structures for the first time. The study is done based on a literature review and field survey. This research reveals that the permanent geometric rules are perfectly used in the design and construction of the prominent domes.

Keywords: geometry in architecture, architectural proportions, prominent domes, iranian golden ratio, geometric proportion

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Authors: Debjani Chakraborty, Abhijit Chatterjee, Aishwaryaprajna

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Posynomials, a special type of polynomials, having singularities, pose difficulties while solving geometric programming problems. In this paper, a methodology has been proposed and used to obtain extreme values for geometric programming problems by nth degree polynomial interpolation technique. Here the main idea to optimise the posynomial is to fit a best polynomial which has continuous gradient values throughout the range of the function. The approximating polynomial is smoothened to remove the discontinuities present in the feasible region and the objective function. This spatial interpolation method is capable to optimise univariate and multivariate geometric programming problems. An example is solved to explain the robustness of the methodology by considering a bivariate nonlinear geometric programming problem. This method is also applicable for signomial programming problem.

Keywords: geometric programming problem, multivariate optimisation technique, posynomial, spatial interpolation

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Authors: K. Khadidja

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Solitons are stable solution of nonlinear Schrodinger equation. Their stability is due to the exact combination between nonlinearity and dispersion which causes pulse broadening. Higher order solitons are born when nonlinear length is N multiple of dispersive length. Soliton order is determined by the number N itself. In this paper, evolution of higher order solitons is illustrated by simulation using Matlab. Results show that higher order solitons change their shape periodically, the reason why they are bad for transmission comparing to fundamental solitons which are constant. Partial analysis of a soliton of higher order explains that the periodic shape is due to the interplay between nonlinearity and dispersion which are not equal during a period. This class of solitons has many applications such as generation of supercontinuum and the impulse compression on the Femtosecond scale. As a conclusion, the periodicity which is harmful to transmission can be beneficial in other applications.

Keywords: dispersion, nonlinearity, optical fiber, soliton

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Authors: Keigo Matsuura, Isao Tomita

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We have studied a method to widen the spectrum of optical pulses that pass through an InGaAsP waveguide for application to broadband optical communication. In particular, we have investigated the competitive effect between spectral broadening arising from nonlinear refraction (optical Kerr effect) and shrinking due to two photon absorption in the InGaAsP waveguide with chi^(3) nonlinearity. The shrunk spectrum recovers broadening by the enhancement effect of the nonlinear refractive index near the bandgap of InGaAsP with a bandgap wavelength of 1490 nm. The broadened spectral width at around 1525 nm (196.7 THz) becomes 10.7 times wider than that at around 1560 nm (192.3 THz) without the enhancement effect, where amplified optical pulses with a pulse width of 2 ps and a peak power of 10 W propagate through a 1-cm-long InGaAsP waveguide with a cross-section of 4 um^2.

Keywords: InGaAsP waveguide, Chi^(3) nonlinearity, spectral broadening, photon absorption

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Authors: Aigul Manapova

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We consider an optimal control problem in the higher coefficient of nonlinear equations with a divergent elliptic operator and unbounded nonlinearity, and the Dirichlet boundary condition. The conditions imposed on the coefficients of the state equation are assumed to hold only in a small neighborhood of the exact solution to the original problem. This assumption suggests that the state equation involves nonlinearities of unlimited growth and considerably expands the class of admissible functions as solutions of the state equation. We obtain formulas for the first partial derivatives of the objective functional with respect to the control functions. To calculate the gradients the numerical solutions of the state and adjoint problems are used. We also prove that the gradient of the cost function is Lipchitz continuous.

Keywords: cost functional, differentiability, divergent elliptic operator, optimal control, unbounded nonlinearity

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Authors: Mohanad Alfach, Amjad Al Helwani

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Post-seismic observations of recent devastating earthquakes have shown that the behavior of the soil-pile-structure shows strong nonlinearity of soil and concrete under intensive seismic loading. Many of pile ruptures recently observed after the strong earthquake due to structural reasons (development of plastic hinges in the piles). The most likely reason for this rupture is the exceeding of maximum bending moment supported by the pile at several points. An analysis of these problems is necessary to take into account the nonlinearity of concrete, the strategy of strengthening the damaged piles and the interaction of these piles with the proposed strengthening by using micropiles. This study aims to investigate the interaction aspects for soil-piles- micropiles-structure using a global approach with a three dimensional finite difference code Flac 3D (Fast lagrangian analysis of continua in 3 dimensions).

Keywords: interaction, piles, micropiles, concrete, seismic, nonlinear, three-dimensional

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Authors: H. Ghodbane, A. A. Taleb, O. Kraa

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This paper presents geometric design of induction heating system. The objective of this design is to improve the temperature distribution in the load. The study of such a device requires the use of models or modeling representation, physical, mathematical, and numerical. This modeling is the basis of the understanding, the design, and optimization of these systems. The optimization technique is to find values of variables that maximize or minimize the objective function.

Keywords: optimization, modeling, geometric design system, temperature increase

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Authors: Yan Lyu, Yiqun Pan, Zhizhong Huang

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In the design stage of a new building, the energy model of this building is often required for the analysis of the performance on energy efficiency. In practice, a certain degree of geometric simplification should be done in the establishment of building energy models, since the detailed geometric features of a real building are hard to be described perfectly in most energy simulation engine, such as ESP-r, eQuest or EnergyPlus. Actually, the detailed description is not necessary when the result with extremely high accuracy is not demanded. Therefore, this paper analyzed the relationship between the error of the simulation result from building energy models and the geometric simplification of the models. Finally, the following two parameters are selected as the indices to characterize the geometric feature of in building energy simulation: the southward projected area and total side surface area of the building, Based on the parameterization method, the simplification from an arbitrary column building to a typical shape (a cuboid) building can be made for energy modeling. The result in this study indicates that this simplification would only lead to the error that is less than 7% for those buildings with the ratio of southward projection length to total perimeter of the bottom of 0.25~0.35, which can cover most situations.

Keywords: building energy model, simulation, geometric simplification, design, regression

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Authors: Boris Melnikov, Ye Zhang, Dmitrii Chaikovskii

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This study explores the pseudo-geometric version of the extensively researched Traveling Salesman Problem (TSP), proposing a novel generalization of existing algorithms which are traditionally confined to the geometric version. By adapting the "onion husk" method and introducing auxiliary algorithms, this research fills a notable gap in the existing literature. Through computational experiments using randomly generated data, several metrics were analyzed to validate the proposed approach's efficacy. Preliminary results align with expected outcomes, indicating a promising advancement in TSP solutions.

Keywords: optimization problems, traveling salesman problem, heuristic algorithms, “onion husk” algorithm, pseudo-geometric version

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Authors: Han Ding, Wang Xiaoliang, Duan Dengping

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During the process of airship design, the layout and the geometric shape of the hull and fins are crucial to the motion characteristics of the airship. In this paper, we obtained the quantification motion sensitivity of the airship to geometric parameters through turning circles and horizontal/vertical zigzag maneuvers by the parameterization of airship shape and building the dynamic model using Lagrangian approach and MATLAB Simulink program. In the dynamics simulation program, the affection of geometric parameters to the mass, center of gravity, moments of inertia, product of inertia, added mass and the aerodynamic forces and moments have been considered.

Keywords: airship, Lagrangian approach, turning circles, horizontal/vertical zigzag maneuvers

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Authors: Xavier Lorang, Ahmadali Tahmasebimoradi, Chetra Mang, Sylvain Girard

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The additive manufacturing processes (e.g. selective laser melting) allow us to produce lattice structures which have less weight, higher impact absorption capacity, and better thermal exchange property compared to the classical structures. Unfortunately, geometric imperfections (defects) in the lattice structures are by-products results of the manufacturing process. These imperfections decrease the lifetime and the strength of the lattice structures and alternate their mechanical responses. The objective of the paper is to present a simulation strategy which allows us to take into account the effect of the geometric imperfections on the mechanical response of the lattice structure. In the first part, an identification method of geometric imperfection parameters of the lattice structure based on point clouds is presented. These point clouds are based on tomography measurements. The point clouds are fed into the platform LATANA (LATtice ANAlysis) developed by IRT-SystemX to characterize the geometric imperfections. This is done by projecting the point clouds of each microbeam along the beam axis onto a 2D surface. Then, by fitting an ellipse to the 2D projections of the points, the geometric imperfections are characterized by introducing three parameters of an ellipse; semi-major/minor axes and angle of rotation. With regard to the calculated parameters of the microbeam geometric imperfections, a statistical analysis is carried out to determine a probability density law based on a statistical hypothesis. The microbeam samples are randomly drawn from the density law and are used to generate lattice structures. In the second part, a finite element model for the lattice structure with the simplified geometric imperfections (ellipse parameters) is presented. This numerical model is used to simulate the generated lattice structures. The propagation of the uncertainties of geometric imperfections is shown through the distribution of the computed mechanical responses of the lattice structures.

Keywords: additive manufacturing, finite element model, geometric imperfections, lattice structures, propagation of uncertainty

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Authors: Zhiming Ye, Dejiang Wang, Huiling Zhao

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Development of the technology demands a higher-level research on the mechanical behavior of materials. Structural members made of bi-modulus materials have different elastic modulus when they are under tension and compression. The stress and strain states of the point effect on the elastic modulus and Poisson ratio of every point in the bi-modulus material body. Accompanied by the uncertainty and nonlinearity of the elastic constitutive relation is the complicated nonlinear problem of the bi-modulus members. In this paper, the small displacement and large displacement finite element method for the bi-modulus members have been proposed. Displacement nonlinearity is considered in the elastic constitutive equation. Mechanical behavior of slender bi-modulus beam-column under different boundary conditions and loading patterns has been simulated by the proposed method. The influence factors on the ultimate bearing capacity of slender beam and columns have been studied. The results show that as the ratio of tensile modulus to compressive modulus increases, the error of the simulation employing the same elastic modulus theory exceeds the engineering permissible error.

Keywords: bi-modulus, ultimate capacity, beam-column, nonlinearity

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