scholarly journals Exact geometry solid-shell element based on a sampling surfaces technique for 3D stress analysis of doubly-curved composite shells

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
G. M. Kulikov ◽  
A. A. Mamontov ◽  
S. V. Plotnikova ◽  
S. A. Mamontov
Keyword(s):  
Stress Analysis ◽  
Numerical Solutions ◽  
Variational Equation ◽  
Shell Element ◽  
Middle Surface ◽  
Superior Performance ◽  
Lagrange Polynomials ◽  
Shell Formulation ◽  
Coarse Meshes ◽  
Doubly Curved

AbstractA hybrid-mixed ANS four-node shell element by using the sampling surfaces (SaS) technique is developed. The SaS formulation is based on choosing inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell in order to introduce the displacements of these surfaces as basic shell variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree In − 1 in the thickness direction for each layer permits the presentation of the layered shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that allows one to minimize uniformly the error due to the Lagrange interpolation. To implement the efficient analytical integration throughout the element, the enhanced ANS method is employed. The proposed hybrid-mixed four-node shell element is based on the Hu-Washizu variational equation and exhibits a superior performance in the case of coarse meshes. It could be useful for the 3D stress analysis of thick and thin doubly-curved shells since the SaS formulation gives the possibility to obtain numerical solutions with a prescribed accuracy, which asymptotically approach the exact solutions of elasticity as the number of SaS tends to infinity.

scholarly journals Exact geometry SaS solid-shell element for 3D stress analysis of FGM piezoelectric structures

2018 ◽  
Vol 5 (1) ◽  
pp. 116-135 ◽  
Author(s):  
G. M. Kulikov ◽  
S. V. Plotnikova
Keyword(s):  
Stress Analysis ◽  
Shell Element ◽  
Middle Surface ◽  
Functionally Graded ◽  
Superior Performance ◽  
Solid Shell ◽  
Lagrange Polynomials ◽  
Graded Material ◽  
Assumed Natural Strain ◽  
Shell Formulation

Abstract A hybrid-mixed functionally graded material (FGM) piezoelectric four-node solid-shell element through the sampling surfaces (SaS) method is proposed. The SaS formulation is based on choosing inside the shell N SaS parallel to the middle surface in order to introduce the displacements and electric potentials of these surfaces as fundamental shell unknowns. Such choice of unknowns with the use of Lagrange polynomials of degree N-1 in through-thickness interpolations of the displacements, strains, electric potential, electric field and material properties leads to a robust FGM piezoelectric shell formulation. The inner SaS are located at Chebyshev polynomial nodes that make it possible to minimize uniformly the error due to Lagrange interpolation. To implement the effective analytical integration throughout the element, the extended assumed natural strain (ANS) method is employed. As a result, the piezoelectric four-node solid-shell element exhibits a superior performance in the case of coarse meshes. To circumvent shear and membrane locking, the hybrid stress-strain solid-shell formulation via the Hu-Washizu variational principle is employed. The developed solid-shell element could be useful for the 3D stress analysis of FGMstructures because the SaS method allows obtaining the solutions with a prescribed accuracy, which asymptotically approach the exact solutions of electroelasticity as the number of SaS tends to infinity.

scholarly journals Modeling and analysis of spiral actuators by exact geometry piezoelectric solid-shell elements

2019 ◽  
Vol 31 (1) ◽  
pp. 53-70
Author(s):  
GM Kulikov ◽  
SV Plotnikova ◽  
E Carrera
Keyword(s):  
Shell Element ◽  
Middle Surface ◽  
Solid Shell ◽  
Modeling And Analysis ◽  
Lagrange Polynomials ◽  
Shell Elements ◽  
Exact Geometry ◽  
Piezoelectric Solid ◽  
Assumed Natural Strain ◽  
Shell Formulation

An exact geometry four-node piezoelectric solid-shell element through the sampling surfaces formulation is proposed. The sampling surfaces formulation is based on choosing inside the shell N – 2 sampling surfaces parallel to the middle surface and located at Chebyshev polynomial nodes to introduce the displacements and electric potentials of these surfaces as fundamental shell unknowns. The bottom and top surfaces are also included into a set of sampling surfaces. Such choice of unknowns with the use of Lagrange polynomials of degree N – 1 in the through-the-thickness interpolations of displacements, strains, electric potential, and electric field yields a robust piezoelectric shell formulation. To implement efficient analytical integration throughout the solid-shell element, the extended assumed natural strain method is employed. The developed hybrid-mixed four-node piezoelectric solid-shell element is based on the Hu-Washizu variational principle and shows the excellent performance for coarse mesh configurations. It can be useful for the 3D stress analysis of piezoelectric shells with variable curvatures, in particular for the modeling and analysis of spiral actuators.

Elastic Analysis of a Skull

1973 ◽  
Vol 40 (4) ◽  
pp. 838-842 ◽  
Author(s):  
C. H. Hardy ◽  
P. V. Marcal
Keyword(s):  
Finite Element ◽  
Composite Material ◽  
Elastic Stress ◽  
Shell Element ◽  
Elastic Analysis ◽  
Triangular Shell Element ◽  
Skull Measurements ◽  
Doubly Curved

A finite-element elastic analysis is made of a skull. Measurements were made of the geometry and thickness of a skull. The skull was then idealized with a doubly curved and arbitrary triangular shell element. Results suggest that the skull is well built for resistance to front loads. The importance of using a composite material through the thickness of the shell was established. On the basis of tensile cracking at maximum elastic stress, loads of 3500 lb and 1400 lb were predicted for the first cracking of the skull due to front and side loading, respectively.

Material Modeling for Autofrettage Stress Analysis Including the “Single Effective Material”

2008 ◽  
Author(s):  
Anthony P. Parker ◽  
Michael C. Gibson ◽  
Amer Hameed ◽  
Edward Troiano ◽  
John G. Hetherington
Keyword(s):  
Stress Analysis ◽  
Numerical Solutions ◽  
Material Behavior ◽  
Material Modeling ◽  
Equivalent Material ◽  
Element Analysis ◽  
Adjustment Procedure ◽  
Analysis Process ◽  
Real Material ◽  
Accurate Procedure

Analytical and numerical stress analysis of the autofrettage process has made great strides in the last few years. The major challenge is no longer the stress analysis process but the incorporation of ‘real’ material behavior, including Bauschinger effect. This means that material properties may vary at every radial location within the tube. In this paper it is demonstrated that Finite Element Analysis (FEA) may be accomplished using a ‘user programmable feature’ within a non-linear FEA or, more simply using an elastic modulus and Poisson’s ratio adjustment procedure within a linear-elastic FEA. The results of these two methods are shown to be in agreement with each other and with an independent numerical analysis. It is further demonstrated that numerical solutions may be obtained using a single ‘fictitious’ material. This is called a ‘single equivalent material’ (SEMAT). Whilst this requires a very small number of iterations for accurate convergence, it dramatically reduces the material-modeling challenges. Furthermore, SEMAT may be implemented into an analytical procedure thereby permitting highly accurate modeling of a real material whose unloading behavior varies with radius. Comparisons indicate that this is a robust, accurate procedure.

scholarly journals A nonlinear rotation-free shell formulation with prestressing for vascular biomechanics

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Nitesh Nama ◽  
Miquel Aguirre ◽  
Jay D. Humphrey ◽  
C. Alberto Figueroa
Keyword(s):  
Degrees Of Freedom ◽  
Shell Element ◽  
Surrounding Tissue ◽  
Triangular Element ◽  
Plane Stress Condition ◽  
Bending Behavior ◽  
Support Conditions ◽  
Shell Formulation ◽  
Constitutive Material

Abstract We implement a nonlinear rotation-free shell formulation capable of handling large deformations for applications in vascular biomechanics. The formulation employs a previously reported shell element that calculates both the membrane and bending behavior via displacement degrees of freedom for a triangular element. The thickness stretch is statically condensed to enforce vessel wall incompressibility via a plane stress condition. Consequently, the formulation allows incorporation of appropriate 3D constitutive material models. We also incorporate external tissue support conditions to model the effect of surrounding tissue. We present theoretical and variational details of the formulation and verify our implementation against axisymmetric results and literature data. We also adapt a previously reported prestress methodology to identify the unloaded configuration corresponding to the medically imaged in vivo vessel geometry. We verify the prestress methodology in an idealized bifurcation model and demonstrate the significance of including prestress. Lastly, we demonstrate the robustness of our formulation via its application to mouse-specific models of arterial mechanics using an experimentally informed four-fiber constitutive model.

Free Vibration Analysis of Double Curvature Thin Walled Structures by a B-Spline Finite Element Approach

2007 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Numerical Solutions ◽  
Free Vibration Analysis ◽  
B Spline ◽  
Thin Walled Structures ◽  
Double Curvature ◽  
Spline Finite Element ◽  
Element Approach ◽  
Shell Formulation

This paper presents a free vibration analysis of general double curvature shell structures using B-spline shape functions and a refinement technique. The shell formulation is developed following the well known Ahmad degenerate approach including the effect of the shear deformation. The formulation is not isoparametric, as a consequence the assumed displacement field is described through non-uniform B-spline functions of any degree. A solution refinement technique is considered by means of a high continuity p-method approach. The eigensolution of a plate, and of single and double curvature shells are obtained by numerical simulation to test the performance of the approach. Solutions are compared with other available analytical and numerical solutions, and discussion follows.

New cubic B-spline approximation technique for numerical solutions of coupled viscous Burgers equations

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Tahir Nazir ◽  
Muhammad Abbas ◽  
Muhammad Kashif Iqbal
Keyword(s):  
Numerical Solutions ◽  
Numerical Study ◽  
Spline Approximation ◽  
Current Approach ◽  
Superior Performance ◽  
Approximation Technique ◽  
Spatial Direction ◽  
Content Type ◽  
B Spline ◽  
Burgers Equations

Purpose The purpose of this paper is to present a new cubic B-spline (CBS) approximation technique for the numerical treatment of coupled viscous Burgers’ equations arising in the study of fluid dynamics, continuous stochastic processes, acoustic transmissions and aerofoil flow theory. Design/methodology/approach The system of partial differential equations is discretized in time direction using the finite difference formulation, and the new CBS approximations have been used to interpolate the solution curves in the spatial direction. The theoretical estimation of stability and uniform convergence of the proposed numerical algorithm has been derived rigorously. Findings A different scheme based on the new approximation in CBS functions is proposed which is quite different from the existing methods developed (Mittal and Jiwari, 2012; Mittal and Arora, 2011; Mittal and Tripathi, 2014; Raslan et al., 2017; Shallal et al., 2019). Some numerical examples are presented to validate the performance and accuracy of the proposed technique. The simulation results have guaranteed the superior performance of the presented algorithm over the existing numerical techniques on approximate solutions of coupled viscous Burgers’ equations. Originality/value The current approach based on new CBS approximations is novel for the numerical study of coupled Burgers’ equations, and as far as we are aware, it has never been used for this purpose before.

Dynamic Buckling of Laminated Anisotropic Spherical Caps

1995 ◽  
Vol 62 (1) ◽  
pp. 13-19 ◽  
Author(s):  
M. Ganapathi ◽  
T. K. Varadan
Keyword(s):  
Time History ◽  
Laminated Composite ◽  
Shell Element ◽  
Dynamic Buckling ◽  
Integration Scheme ◽  
Numerical Integration Scheme ◽  
History Of ◽  
Spherical Caps ◽  
Doubly Curved ◽  
Sudden Jump

The dynamic axisymmetric behavior of clamped laminated composite spherical caps subjected to suddenly applied loads is investigated using an eight-noded quadrilateral doubly curved shear flexible shell element based on the field-consistency approach. Geometric nonlinearity is considered using von Karman’s strain-displacement relations. The solution is obtained using the Wilson-θ numerical integration scheme. The pressure corresponding to a sudden jump in the maximum average deflection in the time history of the shell structure is taken as dynamic buckling pressure. A detailed parametric study is carried out to bring out the effects of shell geometries and material properties, number of layers, lamination schemes, and type of loading on a dynamic buckling load.

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