A Recursive Methodology to Determine the Mechanical Response of Thin Laminated Plates in Bending

Lisbôa, Tales de Vargas; Geiger, Filipe Paixão; Marczak, Rogério José

doi:10.5028/jatm.v9i4.761

Cited by 6 publications

(6 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The matrix operator is decomposed by following a constitutive hierarchy. The requirement (b) is achieved by

d = {boldd}^{(0)} + {boldd}^{(1)} + {boldd}^{(2)} + \dots + {boldd}^{(n)} + \dots,

which, by Equation , can be defined as

bold-italicλ = λ^{(0)} + λ^{(1)} + λ^{(2)} + \dots + λ^{(n)} + \dots,

with the same interpolation functions used for each superposed terms . By applying Equations – into the linear system of Equation , one obtains

[K^{false(iso false)} + K^{false(ani false)}] ({bold-italicλ}^{false(0 false)} + {bold-italicλ}^{false(1 false)} + {bold-italicλ}^{false(2 false)} + \dots + {bold-italicλ}^{false(n false)} + \dots) - f = 0,

which is solved as []

\begin{matrix} right K^{false(iso false)} {bold-italicλ}^{false(0 false)} & = & left boldf, \\ right K^{false(iso false)} {bold-italicλ}^{false(1 false)} & = & left - K^{false(ani false)} {bold-italicλ}^{} \end{matrix}

…”

Section: Adomian Decomposition Methodsmentioning

confidence: 99%

“…with the same interpolation functions used for each superposed terms. [16,27,32] By applying Equations 21-22 into the linear system of Equation 15, one obtains…”

Section: Adomian Decomposition Methodsmentioning

confidence: 99%

“…where correspond to the orthogonal displacements, and denote the in-plane displacements and the rotation around axis and 3 is the transverse displacement. Equation 1 already considers the equivalent single layer hypothesis [2,3,16] : the kinematic plate's behaviour is homogeneous despite the material's heterogeneity. By the linear kinematic relation, the strain field vector ( ) can be obtained with respect to membrane ( ), bending ( ) and transverse shear ( ) strain vectors, written as } .…”

Section: Laminated Thick Plate Equationsmentioning

confidence: 99%

“…The strain energy is linear with respect to , thus = (iso) + (ani) . Consequently, Equation 16 is rewritten as follows…”

Section: Constitutive Decomposition Guided By a Constitutive Hierarchymentioning

confidence: 99%

“…Thai & Choi [15] have developed a FSDT with four unknown functions by assuming that the transverse displacement can be constructed as bending and shear parts and have presented solutions with good correspondence when compared with those found in the literature for antisymmetric cross-ply and angle-ply laminated plates. Lisbôa et al [16] have determined solutions for thin laminated plates by applying the pb-2 RRM with the Adomian Decomposition Method. They have presented solutions for both symmetric and non-symmetric cases with excellent agreement to numeric and analytic solutions.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Application of Adomian‐type method to solve rectangular laminated thick plates in bending

Lisbôa

Marczak

2018

Z Angew Math Mech

Self Cite

View full text Add to dashboard Cite

This paper aims the use of Adomian Decomposition Method along with the pb‐2 Rayleigh‐Ritz Method to obtain the response of thick laminated plates. The Mindlin Plate Theory and the equivalent single layer concept are utilised. The differential operator is decomposed accordingly to a hierarchic constitutive scheme, resulting in a superposition of isotropic and anisotropic constitutive tensors at lamina's level. This implies the superposition of isotropic and a remainder plate stiffness with the latter grouping the anisotropic influence of each lamina at plate's level. By the Adomian Decomposition Method, an isotropic plate solution (related to the isotropic stiffness) is recursively enhanced by the laminae influence (remainder stiffness). Convergence criteria and numeric results are presented, discussed and compared with those found in the literature.

show abstract

“…The matrix operator is decomposed by following a constitutive hierarchy. The requirement (b) is achieved by

d = {boldd}^{(0)} + {boldd}^{(1)} + {boldd}^{(2)} + \dots + {boldd}^{(n)} + \dots,

which, by Equation , can be defined as

bold-italicλ = λ^{(0)} + λ^{(1)} + λ^{(2)} + \dots + λ^{(n)} + \dots,

with the same interpolation functions used for each superposed terms . By applying Equations – into the linear system of Equation , one obtains

[K^{false(iso false)} + K^{false(ani false)}] ({bold-italicλ}^{false(0 false)} + {bold-italicλ}^{false(1 false)} + {bold-italicλ}^{false(2 false)} + \dots + {bold-italicλ}^{false(n false)} + \dots) - f = 0,

which is solved as []

\begin{matrix} right K^{false(iso false)} {bold-italicλ}^{false(0 false)} & = & left boldf, \\ right K^{false(iso false)} {bold-italicλ}^{false(1 false)} & = & left - K^{false(ani false)} {bold-italicλ}^{} \end{matrix}

…”

Section: Adomian Decomposition Methodsmentioning

confidence: 99%

“…with the same interpolation functions used for each superposed terms. [16,27,32] By applying Equations 21-22 into the linear system of Equation 15, one obtains…”

Section: Adomian Decomposition Methodsmentioning

confidence: 99%

Section: Laminated Thick Plate Equationsmentioning

confidence: 99%

“…The strain energy is linear with respect to , thus = (iso) + (ani) . Consequently, Equation 16 is rewritten as follows…”

Section: Constitutive Decomposition Guided By a Constitutive Hierarchymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Application of Adomian‐type method to solve rectangular laminated thick plates in bending

Lisbôa

Marczak

2018

Z Angew Math Mech

Self Cite

View full text Add to dashboard Cite

show abstract

A modified decomposition method to solve linear elliptic partial differential equations in anisotropic domains by enhancing isotropic responses

2019

View full text Add to dashboard Cite

On the development of Adomian decomposition method for solving PDE systems with non-prescribed data

Zeidan

Chau

2022

Comp. Appl. Math.

View full text Add to dashboard Cite

A Recursive Methodology to Determine the Mechanical Response of Thin Laminated Plates in Bending

Cited by 6 publications

References 4 publications

Application of Adomian‐type method to solve rectangular laminated thick plates in bending

Application of Adomian‐type method to solve rectangular laminated thick plates in bending

A modified decomposition method to solve linear elliptic partial differential equations in anisotropic domains by enhancing isotropic responses

On the development of Adomian decomposition method for solving PDE systems with non-prescribed data

Contact Info

Product

Resources

About