Static Response Analysis Research Articles

Wave interaction with Very Large Floating Structure (VLFS) using BEM approach – Revisited

Summary In the present study, a brief discussion on the hydroelastic analysis of VLFS using Boundary Element Method (BEM) with basic assumptions, boundary conditions and support conditions required are presented. An overview of present scenario about development of VLFS using BEM and also future prospects are presented. The study on existing VLFS systems floated in the sea around world could be considered as indicative of the present state of affairs. Further, various numerical methods adopted by the researchers is reviewed in particular, on the hydroelastic analysis of VLFS, dynamic, static and structural response of the system is discussed. The study presented herein will be helpful to naval architects, ocean and structural engineers for suitable design and analysis of VLFS subjected to wave force.

Static response and free vibration analysis of the composite sandwich structures with multi-layer cores

The Layerwise/Solid-Element (LW/SE) method, which was developed based on the layerwise theory and the eight-noded solid element for the laminated composite stiffened plates and sandwich plates in the previous works [1–3], is extended to the static response and free vibration analysis of the composite sandwich structures with multi-layer cores. In the LW/SE method, the layerwise theory is used to model the behavior of the laminated composite facesheets while the eight-noded solid element is employed to discretize the cores. The total governing equations of the composite sandwich plates are assembled by using the compatibility conditions to ensure the compatibility of displacements and the equilibrium conditions to ensure the equilibrium of internal force at the interface between facesheets and cores. In the numerical examples, the static analysis and free vibration analysis of the composite sandwich plates are investigated for the sandwich plates with double-layer honeycombs and pyramidal lattice cores. The proposed method is validated by using the 3D elastic models developed in MSC.Patran/Nastran code. Two kinds of local models of the sandwich plates with double-layer honeycombs are presented for the local response problems to reduce the computational cost in the case of guarantee analysis accuracy of the local response.

Finite Element Modelling for Static and Free Vibration Response of Functionally Graded Beam

A 1D Finite Element model for static response and free vibration analysis of functionally graded material (FGM) beam is presented in this work. The FE model is based on efficient zig-zag theory (ZIGT) with two noded beam element having four degrees of freedom at each node. Linear interpolation is used for the axial displacement and cubic hermite interpolation is used for the deflection. Out of a large variety of FGM systems available, Al/SiC and Ni/Al2O3 metal/ceramic FGM system has been chosen. Modified rule of mixture (MROM) is used to calculate the young's modulus and rule of mixture (ROM) is used to calculate density and poisson's ratio of FGM beam at any point. The MATLAB code based on 1D FE zigzag theory for FGM elastic beams is developed. A 2D FE model for the same elastic FGM beam has been developed using ABAQUS software. An 8-node biquadratic plane stress quadrilateral type element is used for modeling in ABAQUS. Three different end conditions namely simply-supported, cantilever and clamped- clamped are considered. The deflection, normal stress and shear stress has been reported for various models used. Eigen Value problem using subspace iteration method is solved to obtain un-damped natural frequencies and the corresponding mode shapes. The results predicted by the 1D FE model have been compared with the 2D FE results and the results present in open literature. This proves the correctness of the model. Finally, mode shapes have also been plotted for various FGM systems.

Steady state response analysis for fractional dynamic systems based on memory-free principle and harmonic balancing

A semi-analytic approach is proposed to analyze steady state responses of dynamic systems containing fractional derivatives. A major purpose is to efficiently combine the harmonic balancing (HB) technique and Yuan–Agrawal (YA) memory-free principle. As steady solutions being expressed by truncated Fourier series, a simple yet efficient way is suggested based on the YA principle to explicitly separate the Caputo fractional derivative as periodic and decaying non-periodic parts. Neglecting the decaying terms and applying HB procedures result into a set of algebraic equations in the Fourier coefficients. The linear algebraic equations are solved exactly for linear systems, and the non-linear ones are solved by Newton–Raphson plus arc-length continuation algorithm for non-linear problems. Both periodic and triple-periodic solutions obtained by the presented method are in excellent agreement with those by either predictor–corrector (PC) or YA method. Importantly, the presented method is capable of detecting both stable and unstable periodic solutions, whereas time-stepping integration techniques such as YA and PC can only track stable ones. Together with the Floquet theory, therefore, the presented method allows us to address the bifurcations in detail of the steady responses of fractional Duffing oscillator. Symmetry breakings and cyclic-fold bifurcations are found and discussed for both periodic and triple-periodic solutions.

A Theoretical Analysis of Static Response in FG Rectangular Thick Plates with a Four-Parameter Power-Law Distribution

In this paper, we proposed a simple mathematical procedure to solve the differential equations governing the buckling and bending analysis of FG thick rectangular plates resting on two-parametric foundation based on Mindlin assumption. All edges are set on the simply supported conditions. Young modulus of the FG plate was assumed to vary according to a simple four-parameter power law across the thickness direction. For bending analysis, the plate was subjected to two kinds of loading: sinusoidal and uniform. For bucking analysis, two kinds of in-plane loading were applied to the plate: uniaxial and biaxial. Variations of FG material variation profile, thickness ratio, and foundation parameters on buckling critical load and out-plane displacement were examined. The distribution of axial and shear stress across the thickness, when the plate is exposed to uniform transverse loading, was further studied.

A generalized unconstrained theory and isogeometric finite element analysis based on Bézier extraction for laminated composite plates

This work presents an isogeometric finite element formulation based on Bezier extraction of the non-uniform rational B-splines (NURBS) in combination with a generalized unconstrained higher-order shear deformation theory (UHSDT) for laminated composite plates. The proposed approach relaxes zero-shear stresses at the top and bottom surfaces of the plates and no shear correction factors are required. A weak form of static, free vibration and transient response analyses for laminated composite plates is then established and is numerically solved using isogeometric Bezier finite elements. NURBS can be written in terms of Bernstein polynomials and the Bezier extraction operator. IGA is implemented with the presence of C°-continuous Bezier elements which allow to easily incorporate into existing finite element codes without adding many changes as the former IGA. As a result, all computations can be performed based on the basis functions defined previously as the same way in finite element method (FEM). Numerical results performed over static, vibration and transient analysis show high efficiency of the present method.

Static response and stiction analysis of MEMS micromembranes for optical applications

AbstractThe scope of this paper is to investigate the designing, manufacturing and testing of MEMS micromembranes with high mobility. The implementation field of micromembranes is in the optical applications. The mobility of MEMS membranes is provided by the geometry of hinges and their reliability depends on geometrical dimensions and the material behavior. Deformation in different planes of a micromembrane gives the rise to the occurrence of complex efforts that can reduce the operation time especially if one takes into account that, in optical applications, an additional stress state is also given by the thermal effects. Experimental investigations to determine the response of the micromembranes fabricated from gold and with different geometric dimensions are performed by atomic force microscope and nanoindentation. The study of the micromembranes behavior under a mechanical force and different thermal gradients are performed. The temperature is increases from 20 °C to 100 °C. The thermal effect on bending stiffness is observed. Tribological investigations are orientated to adhesion force measurement when the micromembrane is directly deflected to substrate. The results in terms of stiffness agreed with numerical simulation. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The Stability Analysis of the Driving Rod of the Wind Tunnel Test Model Based on Workbench

The ANSYS Workbench is used in this paper to analyse a kind of wind tunnel test model support platform with 5 degrees of freedom. The driving rod of the pitch motion is chosen as the main research project. By using static structural analysis, modal analysis and harmonic response analysis, a detailed analysis is made on the stress, deformation and frequency of the driving rod, and provides theoretical support for the future research on the stability of the institution.

Accurate Response of Wing Structures to Free-Vibration, Load Factors, and Nonstructural Masses

Based on the Carrera unified formulation, this work extends variable kinematic finite beam elements to include load factors and nonstructural masses for the static and vibration analyses of complex, metallic wing structures. According to the Carrera unified formulation, variable kinematic beam theories are formulated in an automatic and hierarchical manner by expressing the displacement field as an arbitrary expansion through generic cross-sectional functions. Both Taylor-like and Lagrange polynomials are used in this paper to develop refined beam kinematics, and the related theories are referred to as Taylor expansion and Lagrange expansion, respectively. The generalized unknowns of Taylor expansion models are the beam axis displacements and the -order displacement derivatives, with being a free parameter of the analysis. Classical beam theories are clearly particular cases of the linear () Taylor expansion model. On the other hand, Lagrange expansion models have only pure translational displacements as unknowns. By exploiting this characteristic of Lagrange expansion, a componentwise approach is implemented and used for the analysis of multicomponent reinforced-shell structures. Numerical applications are developed by classical finite element procedures, and both static response and free vibration analyses are addressed. Various configurations of a benchmark wing are considered, and the capabilities of the present methodologies when dealing with higher-order effects due to deformable cross sections and geometrical discontinuities (for example, underside windows) are evaluated. The attention is focused on the applicability of the present refined beam models to problems involving complex, external inertial loadings. The results are compared to finite element solutions from commercial tools, including full three-dimensional models and models obtained by assembling two-dimensional shell and one-dimensional finite elements.

Static response analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

In this paper, based on the second-order Taylor series expansion and the difference of convex functions algorithm for quadratic problems with box constraints (the DCA for QB), a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods. Although the first-order parameter perturbation method (FM) is effective for solving the static response problem of structures with interval parameters with small uncertainties, the method may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, a new approach (the proposed method:PM) is presented based on the second-order Taylor series expansion and the DCA for QB(the difference of convex functions algorithm for quadratic problems with box constraints).

Collapse Assessment of the Alto Rio Building in the 2010 Chile Earthquake

The 2010 Mw = 8.8 earthquake in Chile subjected thousands of modern buildings to strong shaking. The 15-story, residential, Torre Alto Rio building was the only modern reinforced concrete building over ten stories to collapse. Since the concrete building code used in Chile is based on ACI 318-95, it is a valuable exercise to assess the performance of this building and to identify possible reasons for collapse. Potential reasons for collapse were studied using post-earthquake observed damage, structural drawings, and nonlinear static and dynamic response analyses. Analysis results indicate that collapse was likely influenced by a number of factors, including flexural-compression failure at the web boundary of T-shaped walls below discontinuities on the east side of the building, shear damage in walls across the central corridor at the first level, and tensile fracture and splice failure of the wall boundary and web vertical reinforcement at the ground line on the west side of the building.

An isogeometric finite element approach for three-dimensional static and dynamic analysis of functionally graded material plate structures

This article proposes an efficiently computational tool based on an isogeometric finite element formulation of three-dimensional (3-D) elasticity for static and dynamic response analysis of functionally graded material (FGM) plates. The material properties of FGM plate structures are continuously assumed to vary according to the four-parameter power-law distributions in the thickness direction. The weak form is discretized and approximated by NURBS-based isogeometric approach. The method allows us to preserve exact geometry and is flexible to employ higher-order approximations for the desired accuracy. Through numerical tests, a quartic NURBS element is strongly recommended for eliminating naturally shear locking. Moreover, this element can produce an ultra-accurate solution with a low number of degrees of freedom. Numerical validation shows excellent performance of the present method in comparison with other available methods.

Unusual magnetic damping effect in a silver–cobalt ferrite hetero nano-system

The analysis of static and dynamic magnetic response of CoFe2O4–Ag hetero nano-system revealed, with the aid of micromagnetic simulations, a severe alteration of the magnetic relaxation behaviour of CoFe2O4 upon interaction with non-magnetic Ag.

Performance Analysis of Wind-Induced Piezoelectric Vibration Bimorph Cantilever for Rotating Machinery

Harvesting the energy contained in the running environment of rotating machinery would be a good way to supplement energy to the wireless sensor. In this paper, we take piezoelectric bimorph cantilever beam with parallel connection mode as energy collector and analyze the factors which can influence the generation performance. First, a modal response theory model is built. Second, the static analysis, modal analysis, and piezoelectric harmonic response analysis of the wind-induced piezoelectric bimorph cantilever beam are given in detail. Finally, an experiment is also conducted. The results show that wind-induced piezoelectric bimorph cantilever beam has low resonant frequency and stable output under the first modal mode and can achieve the maximum output voltage under the resonant condition. The output voltage increases with the increase of the length and width of wind-induced piezoelectric bimorph cantilever beam, but the latter increasing amplitude is relatively smaller. In addition, the output voltage decreases with the increase of the thickness and the ratio of metal substrate to piezoelectric patches thickness. The experiment showed that the voltage amplitude generated by the piezoelectric bimorph cantilever beam can reach the value simulated in ANSYS, which is suitable for actual working conditions.

Finite Element Analysis of Guyed Offshore Monotower Subjected to Extreme Environment in Malaysian Water

This paper presents the finite element structural sensitivity analysis of a cable guyed monotower known as the Tarpon Monopod when subjected to extreme environments in Malaysian waters. A hydrodynamic loading and static platform response analysis is performed in SACS v5.3 to gauge the structural robustness in extreme Malaysian metocean conditions. A Stokes Fifth Order Wave Theory was employed to obtain wave kinematics and dynamics for load computation. The Tarpon Monopod design is reviewed generically. An actual platform located in 60m water depth within Malaysian waters is modelled for analysis. Four different guying cable scenarios are considered which are the fully guyed condition (three guy cables pinned), two guy cables condition (one wire loss), one guy cable condition (two wire loss) and free standing condition (total loss of guy wires) are presented. The environmental load sets are simulated at different headings using 45 degree steps. The results suggest that the structural caisson contributes little to the lateral stiffness of the platform. The Tarpon Monopod has little structural redundancy and its integrity is highly dependent on guy wire condition and environmental load headings.

Axiomatic/Asymptotic Technique Applied to Refined Theories for Piezoelectric Plates

This article is devoted to the evaluation of refined theories for static response analysis of piezoelectric plate. The Carrera Unified Formulation (CUF) is employed to generate the refined plate models. The CUF allows the hierarchical implementation of refined models based on any-order expressions of the unknown variables. Equivalent single layer (ESL) and layerwise (LW) approaches are used to generate the refined models. The governing equations are obtained considering Navier-type, closed-form solutions. The axiomatic/asymptotic technique is employed in order to evaluate the relevance of each model term. This technique computes the relevance of a model term by measuring the error introduced with its deactivation with respect to a reference solution. The axiomatic/asymptotic technique is applied considering the sensor and actuator configurations for piezoelectric plates. Moreover, the analyses are performed taking into account the influence of the length-to-thickness ratio (a/h) and the use of isotropic or orthotropic materials. “Best” models are proposed and the stress/displacement components and electric potential distributions are evaluated by means of these reduced models.

Wind-Induced Dynamic Analysis of Rung-Shape Long-Span Tensile Cable Membrane Structure

The rung-shape long-span tensile cable-membrane structure in Foshan Century Lotus Stadium was analyzed. The effects of different pre-stressing degree and membrane tensile rigidity were discussed on structure natural vibration, static wind loads response and wind-induced dynamic analysis. Dynamic wind equivalent coefficient which can be used in structural design was also preliminary analyzed.

Design and analysis of bidirectional deployable parabolic cylindrical antenna

A bidirectional deployable parabolic cylindrical reflector for an L-band synthetic aperture radar is presented in this study, in which a self-deployed antenna with low weight was designed. The antenna consists of four curved surfaces formed from thin sheets of composite materials connected by hinges along the edges, and the reflective surface is provided by the front surface. The edge profiles of connecting lines were obtained through geometric analysis. A scaled model, including design and manufacture, was demonstrated to validate the process from the folded state to the fully deployed state. The non-contact synchronous vision measuring method was used to test the basic frequency of the scaled model, and the test results gave the verification of the analyses. Compared with the existing unidirectional deployable antenna, this new type of bidirectional deployable antenna can be applied to larger-size antennas and has better performance because the glass-woven tape connections were substituted with more reliable hinges. Static, modal, harmonic response, and transient response analyses of the full-sized reflector structure were modeled with the commercial finite element (FE) package ABAQUS. The modeling techniques were developed to predict the structural dynamic behavior of the reflector and the results showed that the first natural frequency was 0.865 Hz, and the reflector structure had good stiffness in three directions. This proposed structure has very high stiffness-to-mass ratio because of its hollow solid construction. A preliminary simulation of radiation properties of the parabolic cylindrical antenna, fed by an off-set linear feed horn array, was conducted to obtain the radiation pattern of the feed and the reflector.

Finite Element Modeling of Optical Path Length Control Device for Laser Gyroscope

Optical path length variations due to temperature, manufacturing misalignments, operation environments can affect the performance of ring laser gyroscope (RLG). This paper presents a structural design of optical path length control device (PLC) using finite element analysis. The static analysis and harmonic response analysis of the PLC is performed to investigate the deformation on different voltage, and model analysis is selected to determine the natural frequency and eigenmodes. To validate the simulation results, an experiment on RLG with mode-scanning is carried out and the maximum errors are within 0.025um. The experiment results are found to be in good agreement with the simulation results. The results indicate that the finite element model can be beneficial to designing and optimizing the structural parameters for the PLC.

Transformed perturbation stochastic finite element method for static response analysis of stochastic structures

To obtain the probability density functions and the cumulative distribution functions of static responses of stochastic structures, a hybrid stochastic method named as the transformed perturbation stochastic finite element method (TPSFEM) is proposed. In TPSFEM, the static responses of stochastic structures are approximated as the linear functions of random variables by using the first order perturbation technique. According to the approximated linear relationships between static responses and random variables, the probability density functions of static responses are obtained by the change-of-variable technique. The cumulative distribution functions of static responses are calculated by the numerical integration method. The numerical examples on a thin plate, a six-bar truss structure, a Mindlin plate and a shell structure verify the effectiveness and accuracy of the proposed method. Hence, the proposed method can be considered as an alternative engineering method for the static response analysis of stochastic structures.