uni seminar
TRANSCRIPT
Advanced FEACoded in Matlab
JL Mantari, PhD
Contents• Plates theories
• Accuracy problem
• New theories
• FEA simple applications
• FEA layerwise
• FEA applications
Plate theories Existing theories
CPT (Classical plate theory), based on the assumptions of Kirchhoff’s plate theory.
FSDT (First order shear deformation theory), assumes constant transverse shear deformation and violates free surface boundary conditions.
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HSDT (Higher order shear deformation theory), assumes adequate transverse shear deformation and comply free surface boundary conditions.
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3*
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Plate theories Existing theories
ESL (Equivalent single layer) theories: CPT (Classical plate theory),FSDT (First shear deformation theory),HSDT (Higher order shear deformation theory),Others
Plate theories Existing theories
Layerwise theories:FSDTHSDTOthers
Plate theories Existing theories
Plate theories Accuracy problem
For unstiffened and stiffened ship type structures, HSDTs should be used because the deformation field is close to the deformation in real situation.
Variation of central deflection (mm) with varying geometric configurations
HSDTs
Plate theories Well-know HSDTs
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Plate theories New GHSDTs
,
,
.
GHSDT1
GHSDT2
FEA Simple applications
Plates special case of shells. Beams special case of plates. Then, curved beams are special case of shells!
Beams Plates
Shells FGP
FEA bases A unified theory
,
,
.
Assume the following displacement field to begin the derivation of the unified theory I.
Laminate analysis. Steps for the validation of the theory
,
,
.
Displacement field.Elasticity theory to get strains.Law of Hook to get stresses.The principle of virtual work and the variational theory to get,A set of differential equations that govern the plate and finally,Solve it with an appropriated solution (closed-form).
D E L T A S
Laminate analysis. Finite element method
,
,
.
Displacement field.Elasticity theory to get strains.Law of Hook to get stresses.The principle of virtual work, then use the discretization.Apply boundary conditions, and finallySolve it!
D E L T A S
1. When ESL FE codes are implemented by using: FSDT
A (Cº) FEM code can be implemented Requires arbitrary shear correction factors No comply free surface boundary condition
HSDT A (C ) FEM need to be implemented Normally non-conforming FEM are implementedA (Cº) FEM code can be also achieved
2. FEM using FSDT and HSDT have been explored since 1960s.
3. Layerwise FE codes do not need shear correction factors as some well-know ESL HSDT.
4. A new generalized layerwise HSDT is presented in this thesis.
Laminate analysis. Existing theories (FEM)
Laminate analysis. Trigonometric layerwise HSDT(FEM)
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Laminate analysis. Generalized layerwise HSDT
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Laminate analysis. Reducing DOFs
Shear continuity imposed
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Laminate analysis. Energy principle (FEM)
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Four-nodded quadrilateral Cº continuous isoparametric element with five-degrees-of-freedom (shear continuity is imposed)
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Laminate analysis. Applications
Beams Plates
Stiffened plates FGP