Influence of Joint Flexibility on Vibration Analysis of Free-Free Beams

AbstractIn present work, joint flexibility (or looseness) of the free-free beam is investigated by using a two noded beam finite element formulation with transverse displacement and joint rotations as the degrees of freedom per node at joint location. Flexibility of the joint is primarily represented by means of a rotational spring analogy, where the stiffness of the rotational spring characterizes the looseness of the flexible joint for an applied bending moment. Influence of joint location as well as joint stiffness on modal behavior of first five modes of slender, uniform free-free beams are discussed for various values of non-dimensional rotational spring stiffness parameter. Numerical accuracy of the results obtained from the present finite element formulation are validated by using the commercially available finite element software which shows the confidence gained on the numerical results discussed in the present study.

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Generalized finite element formulation for efficient first-order plastic hinge analysis

Advances in Mechanical Engineering ◽

10.1177/1687814019836366 ◽

2019 ◽

Vol 11 (3) ◽

pp. 168781401983636

Author(s):

Dae-Jin Kim ◽

Hong-Jun Son ◽

Yousun Yi ◽

Sung-Gul Hong

Keyword(s):

Finite Element ◽

Degrees Of Freedom ◽

Plastic Hinge ◽

Computational Cost ◽

Finite Element Formulation ◽

Solution Technique ◽

Element Formulation ◽

Plastic Hinges ◽

First Order ◽

Generalized Finite Element

This article presents generalized finite element formulation for plastic hinge modeling based on lumped plasticity in the classical Euler–Bernoulli beam. In this approach, the plastic hinges are modeled using a special enrichment function, which can describe the weak discontinuity of the solution at the location of the plastic hinge. Furthermore, it is also possible to insert a plastic hinge at an arbitrary location of the element without modifying its connectivity or adding more elements. Instead, the formations of the plastic hinges are achieved by hierarchically adding more degrees of freedom to existing elements. Due to these features, the proposed methodology can efficiently perform the first-order plastic hinge analysis of large-frame structures. A generalized finite element solution technique based on the static condensation scheme is also proposed in order to reduce the computational cost of a series of linear elastic problems, which is in general the most time-consuming portion of the first-order plastic hinge analysis. The effectiveness and accuracy of the proposed method are verified by analyzing several representative numerical examples.

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The displacement view of a multilayered HSDT plate

Journal of Polymer Science and Engineering ◽

10.24294/jpse.v1i2.863 ◽

2018 ◽

Vol 1 (2) ◽

Author(s):

Priyaranjan Pal

Keyword(s):

Finite Element ◽

Degrees Of Freedom ◽

Shear Deformation Theory ◽

Mesh Size ◽

Finite Element Formulation ◽

Computational Time ◽

Element Formulation ◽

Maximum Deflection ◽

Suitable Combination ◽

Optimal Mesh

This paper presents the state of displacement of a multilayered composite laminate subjected to transverse static load with varying balance, symmetric and anti-symmetric angle-ply and cross-ply staking sequences. Higher-order shear deformation theory (HSDT) is considered in the finite element formulation of nine-noded isoparametric element with seven degrees of freedom at each node. The finite element formulation is transformed into computer codes. A convergence study is carried out first to obtain the optimal mesh size for minimizing the computational time. The maximum deflection at the center of plate for both fixed and simply supported edges is verified with reported literature and a good conformity is found. An attempt has been made to observe the minimum value of maximum deflection in the laminate for attaining the maximum strength of laminate with a suitable combination of stacking sequences with a constant volume of material.

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Static and dynamic analyses of functionally graded sandwich skew shell panels

Journal of Sandwich Structures & Materials ◽

10.1177/1099636220983653 ◽

2021 ◽

pp. 109963622098365

Author(s):

Shashank Pandey ◽

S Pradyumna ◽

Shakti Singh Gupta

Keyword(s):

Finite Element ◽

Pure Metal ◽

Functionally Graded ◽

Thickness Ratio ◽

Finite Element Formulation ◽

Element Formulation ◽

Transverse Displacement ◽

Skew Angle ◽

The Core ◽

Dynamic Analyses

The present work is an attempt to develop a simple, accurate and widely applicable finite element formulation having a C0 continuity of transverse displacement at nodes, for static and dynamic analyses of functionally graded sandwich skew shell (FGSSS) panels. A layerwise displacement field based on first-order shear-deformation theory for each layer along with Sanders’ approximation has been adopted for the analysis. Compatibility conditions are imposed at the layer interfaces to satisfy displacement continuity. Two different configurations of FGSSS are taken up in the present investigation. In the first configuration, the top and bottom layers of the panel are made of functionally graded material (FGM) and the core is made of pure metal, whereas in the second configuration, the top and bottom layers are made of pure ceramic and pure metal, respectively and the core is considered to be made of FGM. The material properties of both configurations of FGM panels are estimated according to the rule of mixture. It is observed from the analysis that the present finite element formulation is simple, accurate and computationally efficient. Parameters like skew angle, span to thickness ratio, core to facesheet thickness ratio, volume fraction and boundary conditions have a significant effect on static and dynamic behavior of functionally graded sandwich skew shell panels.

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Advanced Finite Element Formulation for Piezoelectric Smart Shell Structures Under Consideration of Geometrical Nonlinearity

Volume 12: Mechanics of Solids, Structures and Fluids ◽

10.1115/imece2008-67335 ◽

2008 ◽

Author(s):

Katrin Schulz ◽

Sven Klinkel ◽

Werner Wagner

Keyword(s):

Finite Element ◽

Electric Potential ◽

Degrees Of Freedom ◽

Geometrical Nonlinearity ◽

Shell Element ◽

Shell Structures ◽

Finite Element Formulation ◽

Element Formulation ◽

Displacement Fields ◽

Piezoelectric Structures

A geometrically nonlinear highly accurate finite element formulation to analyze piezoelectric shell problems is presented. The formulation is based on the mixed field variational principle of Hu-Washizu including the independent fields displacements, electric potential, strains, electric field, mechanical stresses and dielectric displacements. The normal zero stress condition and the normal zero dielectric displacement condition for shells are enforced by the independent resultant stress and resultant dielectric displacement fields. The arbitrary reference surface of the shell is modeled with a four node element. Each node possesses six mechanical degrees of freedom, three displacements and three rotations, and one electrical degree of freedom, which is the difference of the electric potential through the shell thickness. The developed shell element fulfills the patchtests and is able to model arbitrary curved shell structures. Some numerical examples demonstrate the applicability of the present shell element for piezoelectric systems and integrated piezoelectric structures.

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