scholarly journals Design space for bifurcation buckling of laser-welded web-core sandwich plates as predicted by classical and micropolar plate theories

2020 ◽  
Author(s):  
Jani Romanoff ◽  
Anssi Karttunen ◽  
Petri Varsta
Keyword(s):  
Differential Equations ◽  
Structural Engineering ◽  
Design Space ◽  
Plate Theory ◽  
Sandwich Panels ◽  
Design Stage ◽  
Biaxial Compression ◽  
Sandwich Plates ◽  
Aspect Ratios ◽  
Micropolar Plate

Abstract The strength of laser-welded web-core sandwich plates is often limited by buckling. In design of complex thin-walled structures the combination of possible structural and material combinations is basically infinite. The feasibility of these combinations can be assessed by using analytical, numerical and experimental methods. At the early design stages such as concept design stage, the role of analytical methods is significant due to their capability for parametric description and extremely low computational efforts once the solutions have been established for prevailing differential equations. Over the recent years significant advances have been made on analytical strength prediction of web-core sandwich panels. Therefore, aim of the present paper is to show impact of this development to the design space of web-core sandwich panels in buckling. The paper reviews first, briefly the differential equations of a 2-D micropolar plate theory for web-core sandwich panels and the Navier buckling solution for biaxial compression recently derived by Karttunen et al. (Int J Solids Struct 170(1):82–94, 2019) by exploiting energy methods. By comparing the micropolar and widely-used classical first-order shear deformation plate theory (FSDT) solutions, it is shown that the different equivalent single layer (ESL) formulations and plate aspect ratios have a significant impact on the practical outcomes of the feasible design space and this way motivating further developments for micropolar formulations from practical structural engineering viewpoint.

Design Optimization of Steel Sandwich Hoistable Car Decks Applying Homogenized Plate Theory

2008 ◽  
Vol 24 (02) ◽  
pp. 108-115
Author(s):  
Jani Romanoff ◽  
Alan Klanac
Keyword(s):  
Genetic Algorithm ◽  
Structural Optimization ◽  
Design Optimization ◽  
Plate Theory ◽  
Sandwich Panels ◽  
Sandwich Plates ◽  
Concept Design ◽  
Bending Response

This paper describes an approach for concept design of laser-welded web-core steel sandwich panels. The method uses a newly developed theory for the bending response of laser-welded web-core sandwich plates. Structural optimization is carried out using enumeration and newly developed vectorization-based genetic algorithm. To demonstrate these concepts, a case study in design of a hoistable car deck is considered. Finally, the optimization is conducted considering the objectives of deck weight.

Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates

2012 ◽  
Vol 28 (3) ◽  
pp. 439-452 ◽  
Author(s):  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Power Law ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Equilibrium Equations ◽  
Graded Material ◽  
Plate Aspect Ratio ◽  
Type V ◽  
Power Law Index

AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

Characterization of the vibration, stability and static responses of graphene-reinforced sandwich plates under mechanical and thermal loadings using the refined shear deformation plate theory

2021 ◽  
pp. 109963622199386
Author(s):  
Hessameddin Yaghoobi ◽  
Farid Taheri
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Sheet Thickness ◽  
Analytical Investigation ◽  
Sandwich Plates ◽  
Simply Supported ◽  
Vibration Stability ◽  
Shear Deformation Plate Theory

An analytical investigation was carried out to assess the free vibration, buckling and deformation responses of simply-supported sandwich plates. The plates constructed with graphene-reinforced polymer composite (GRPC) face sheets and are subjected to mechanical and thermal loadings while being simply-supported or resting on different types of elastic foundation. The temperature-dependent material properties of the face sheets are estimated by employing the modified Halpin-Tsai micromechanical model. The governing differential equations of the system are established based on the refined shear deformation plate theory and solved analytically using the Navier method. The validation of the formulation is carried out through comparisons of the calculated natural frequencies, thermal buckling capacities and maximum deflections of the sandwich plates with those evaluated by the available solutions in the literature. Numerical case studies are considered to examine the influences of the core to face sheet thickness ratio, temperature variation, Winkler- and Pasternak-types foundation, as well as the volume fraction of graphene on the response of the plates. It will be explicitly demonstrated that the vibration, stability and deflection responses of the sandwich plates become significantly affected by the aforementioned parameters.

A convenient formulation of Sadowsky's model for elastic ribbons

2021 ◽  
Vol 477 (2255) ◽  
Author(s):  
Sébastien Neukirch ◽  
Basile Audoly
Keyword(s):  
Differential Equations ◽  
Constitutive Relation ◽  
Classical Problem ◽  
Constitutive Law ◽  
System Of Differential Equations ◽  
Dimensional Model ◽  
Simple Method ◽  
One Dimensional ◽  
Aspect Ratios ◽  
Nonlinear Constitutive Relation

Elastic ribbons are elastic structures whose length-to-width and width-to-thickness aspect ratios are both large. Sadowsky proposed a one-dimensional model for ribbons featuring a nonlinear constitutive relation for bending and twisting: it brings in both rich behaviours and numerical difficulties. By discarding non-physical solutions to this constitutive relation, we show that it can be inverted; this simplifies the system of differential equations governing the equilibrium of ribbons. Based on the inverted form, we propose a natural regularization of the constitutive law that eases the treatment of singularities often encountered in ribbons. We illustrate the approach with the classical problem of the equilibrium of a Möbius ribbon, and compare our findings with the predictions of the Wunderlich model. Overall, our approach provides a simple method for simulating the statics and the dynamics of elastic ribbons.

Nonlinear Vibration Analysis of Viscoelastic Smart Sandwich Plates Through the use of Fractional Derivative Zener Model

2021 ◽  
pp. 2150061
Author(s):  
Hamid Reza Talebi Amanieh ◽  
Seyed Alireza Seyed Roknizadeh ◽  
Arash Reza
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Nonlinear Vibration ◽  
Fractional Order ◽  
Sandwich Plate ◽  
Functionally Graded ◽  
Viscoelastic Layer ◽  
Sandwich Plates ◽  
Multiple Time ◽  
Nonlinear Frequency

In this paper, the nonlinear vibrational behavior of a sandwich plate with embedded viscoelastic material is studied through the use of constitutive equations with fractional derivatives. The studied sandwich structure is consisted of a viscoelastic core that is located between the faces of functionally graded magneto-electro-elastic (FG-MEE). In order to determine the frequency-dependent feature of the viscoelastic layer, four-parameter fractional derivative model is utilized. The material properties of FG-MEE face sheets have been distributed considering the power law scheme along the thickness. In addition, for derivation of the governing equations on the sandwich plate, first-order shear deformation plate theory along with von Karman-type of kinematic nonlinearity are implemented. The derived partial differential equations (PDEs) have been transformed to the ordinary differential equations (ODEs) through the Galerkin method. After that, the nonlinear vibration equations for the sandwich plate have been solved by multiple time scale perturbation technique. Moreover, for evaluating the effect of different parameters such as electric and magnetic fields, fractional order, the ratio of the core-to-face thickness and the power low index on the nonlinear vibration characteristics of sandwich plates with FG-MEE face sheets, the parametric analysis has been performed. The obtained results revealed the enhanced nonlinear natural frequency through an increment in the fractional order. Furthermore, the prominent influence of fractional order on the nonlinear frequency of sandwich plate was declared at the negative electric potential and positive magnetic potential.

Calculation for Elastic Global Buckling of Sandwich Plates with Ribs

2012 ◽  
Vol 188 ◽  
pp. 25-30 ◽  
Author(s):  
Qi Chao Xue ◽  
Guang Ping Zou ◽  
Ye Wu ◽  
Hai Lin Xiong ◽  
Meng Chai
Keyword(s):  
Energy Method ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Sandwich Plates ◽  
Buckling Stress ◽  
Global Buckling ◽  
Simple Support ◽  
Rectangular Sandwich Plate ◽  
Two Sides ◽  
Rectangular Sandwich Plates

Based on Reissner’s sandwich plate theory, the critical globlal buckling equation of sandwich plate with ribs is deduced by energy method under simple support boundary conditions. And the critical buckling solution is obtained and discussed here. Afterwards a rectangular sandwich plate with steel faceplate and polyurthane core is taken as an example. The influence on critical global buckling stress with different inertia moments in rectangular sandwich plates are discussed. simularly the effect of the lengh ratio of two sides and the thickness of rectangular sandwich plate are also studied.

scholarly journals Investigations of the Effects of Geometric Imperfections on the Nonlinear Static and Dynamic Behavior of Capacitive Micomachined Ultrasonic Transducers

Micromachines ◽  
2018 ◽  
Vol 9 (11) ◽  
pp. 575 ◽  
Author(s):  
Aymen Jallouli ◽  
Najib Kacem ◽  
Joseph Lardies
Keyword(s):  
Differential Equations ◽  
Dynamic Behavior ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Ultrasonic Transducers ◽  
Initial Deflection ◽  
Geometric Imperfections ◽  
Resonance Frequencies

In order to investigate the effects of geometric imperfections on the static and dynamic behavior of capacitive micomachined ultrasonic transducers (CMUTs), the governing equations of motion of a circular microplate with initial defection have been derived using the von Kármán plate theory while taking into account the mechanical and electrostatic nonlinearities. The partial differential equations are discretized using the differential quadrature method (DQM) and the resulting coupled nonlinear ordinary differential equations (ODEs) are solved using the harmonic balance method (HBM) coupled with the asymptotic numerical method (ANM). It is shown that the initial deflection has an impact on the static behavior of the CMUT by increasing its pull-in voltage up to 45%. Moreover, the dynamic behavior is affected by the initial deflection, enabling an increase in the resonance frequencies and the bistability domain and leading to a change of the frequency response from softening to hardening. This model allows MEMS designers to predict the nonlinear behavior of imperfect CMUT and tune its bifurcation topology in order to enhance its performances in terms of bandwidth and generated acoustic power while driving the microplate up to 80% beyond its critical amplitude.

In-Plane Pre-Stress Analysis for Automotive Airbag Electronic Control Unit’s Printed Circuit Board Transverse Vibration

2018 ◽  
Author(s):  
Guo Xiaochuan
Keyword(s):  
Simulation Model ◽  
Transverse Vibration ◽  
Printed Circuit Board ◽  
Plate Theory ◽  
Circuit Board ◽  
Structural Vibration ◽  
Design Stage ◽  
Electronic Control ◽  
Component Level ◽  
Printed Circuit

For design of automotive airbag electronic control units (AB ECU), it is essential to have a validated and reliable finite element (FE) simulation model in place in order to allow already in an early design stage for the accurate prediction of the ECU’s structural vibration behavior. A “bottom-up” approach which described in the ASME guide for verification and validation (ASME V&V 10-2006) is applied for the validation of the AB ECU simulation model. The AB ECU is decomposed into different assembly level. Single printed circuit board (PCB) is the lowest elementary component level. In the PCB level simulation and validation, the influence of in-plane pre-stress on PCB’s transverse vibration characteristic has been encountered, but it has been found out that the source of the in-plane pre-stress can not be explained by classical beam/plate theory. Analysis and simulation for PCB fixation reveals that the fundamental source of the in-plane pre-stress is structure’s geometric nonlinearity.

On the buckling of advanced composite sandwich rectangular plates

2020 ◽  
pp. 109963622092508 ◽  
Author(s):  
Atteshamuddin S Sayyad ◽  
Yuwaraj M Ghugal
Keyword(s):  
Shear Deformation ◽  
Power Law ◽  
Analytical Solutions ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Skin Thickness ◽  
Sandwich Plates ◽  
Rectangular Plates ◽  
Aspect Ratios

In this paper, higher order closed-formed analytical solutions for the buckling analysis of functionally graded sandwich rectangular plates are obtained using a unified shear deformation theory. Three-layered sandwich plates with functionally graded skins on top and bottom; and isotropic core in the middle are considered for the study. The material properties of skins are varied through the thickness according to the power-law distribution. Two types of sandwich plates (hardcore and softcore) are considered for the detail numerical study. A unified shear deformation theory developed in the present study uses polynomial and non-polynomial-type shape functions in terms of thickness coordinate to account for the effect of shear deformation. In the present theory, the in-plane displacements consider the combined effect of bending rotation and shear rotation. The parabolic shear deformation theory of Reddy and the first-order shear deformation theory of Mindlin are the particular cases of the present unified formulation. The governing differential equations are evaluated from the principle of virtual work. Closed-formed analytical solutions are obtained by using the Navier’s technique. The non-dimensional critical buckling load factors are obtained for various power-law coefficients, aspect ratios and skin-core-skin thickness ratios.

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