Completely hierarchical p-version curved shell element for laminated composite plates and shells

Surana, Karan S.; Sorem, Robert M.

doi:10.1007/bf00370038

Cited by 15 publications

(6 citation statements)

References 28 publications

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“…Secondly, consideration of thermal effects requires consideration of energy equation (98) which is not possible in energy methods or principle of virtual work. Nonetheless, if we limit the physics to conform to what has been considered in reference [39] [40], then the mathematical model (96) -(100) obviously reduces to (101) and (102).…”

Section: Final Mathematical Model (Thermoelastic)mentioning

confidence: 99%

“…Thus, for such deformation physics one could derive the finite element formulation directly using principle of virtual work or energy method. This in fact has been done in reference [39] [40] for three dimensional laminated composite curved shell elements. A serious drawback of this approach is that, in this approach only the equations corresponding to balance of linear momenta can be derived.…”

Section: Plate and Shell Element Geometry And Local Approximationmentioning

confidence: 99%

“…Obviously, the mathematical model used currently consisting of (5) -(9) is not the same as derived here using NCCM consisting of Equations(39),(40), (48) -(50).2) The balance of linear momenta (39) contain usual terms related to the gradients of the stress tensor σ . σ is due to Cauchy moment tensor (necessitated due to the presence of internal rotations).4) The moment tensor m is symmetric due to balance of moment of moments balance law [37] [38] necessary in NCCM.…”

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confidence: 99%

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Thermodynamic Consistency of Plate and Shell Mathematical Models in the Context of Classical and Non-Classical Continuum Mechanics and a Thermodynamically Consistent New Thermoelastic Formulation

Surana¹,

Mathi²

2020

AJCM

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Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler's equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic as

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Section: Final Mathematical Model (Thermoelastic)mentioning

confidence: 99%

Section: Plate and Shell Element Geometry And Local Approximationmentioning

confidence: 99%

mentioning

confidence: 99%

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Thermodynamic Consistency of Plate and Shell Mathematical Models in the Context of Classical and Non-Classical Continuum Mechanics and a Thermodynamically Consistent New Thermoelastic Formulation

Surana¹,

Mathi²

2020

AJCM

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“…Since the advent of p-version of finite element method (earlier works can be found in references [24]- [35]), its application for solving laminated composite problems grew. More recently the p-version hierarchical finite element method has been applied to plates and shells as well as beams including laminated composites in references [36] [37] [38] [39]. In these works, hierarchical p-approximation for displacements is used in the direction transverse to the plane of the laminate.…”

Section: Literature Reviewmentioning

confidence: 99%

“…If the matter is non-isotropic and when the constitutive theory for σ in terms of ε is like (32)-(36), then in the energy functional I (37) there is no basis for [ ]…”

mentioning

confidence: 99%

Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and Non-Homogeneous Non-Isotropic Solid Continua

Surana¹,

Alverio²

2020

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Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (I) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (δI) set to zero is a necessary con-How to cite this paper: Surana, K.S. and Alverio, E.N. (2020) Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and

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p-Version two-dimensional curved beam element using piecewise hierarchical approximation for laminated composites

Orth

Surana

1993

Computational Mechanics

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Completely hierarchical p-version curved shell element for laminated composite plates and shells

Cited by 15 publications

References 28 publications

Thermodynamic Consistency of Plate and Shell Mathematical Models in the Context of Classical and Non-Classical Continuum Mechanics and a Thermodynamically Consistent New Thermoelastic Formulation

Thermodynamic Consistency of Plate and Shell Mathematical Models in the Context of Classical and Non-Classical Continuum Mechanics and a Thermodynamically Consistent New Thermoelastic Formulation

Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and Non-Homogeneous Non-Isotropic Solid Continua

p-Version two-dimensional curved beam element using piecewise hierarchical approximation for laminated composites

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