Fast assembly of Galerkin matrices for 3D solid laminated composites using finite element and isogeometric discretizations

Antolín, Pablo

doi:10.1007/s00466-019-01756-6

Cited by 7 publications

(4 citation statements)

References 70 publications

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“…Even though, the original designation of the component-free approach was "B free", the authors of the present manuscript consider appropriate to adjust the given name to "component-free" formulation, to further clarify that the proposed formulation is not only free from the so-called B and D matrix, but, what is further more paramount, from any basis, axes or components, being the key ingredient of the propose approach. The "B free" finite element approach has been also adopted in [1,20,21,32,39].…”

Section: Introductionmentioning

confidence: 99%

A component-free Lagrangian finite element formulation for large strain elastodynamics

et al. 2021

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Standard finite element formulation and implementation in solid dynamics at large strains usually relies upon and indicial-tensor Voigt notation to factorized the weighting functions and take advantage of the symmetric structure of the algebraic objects involved. In the present work, a novel component-free approach, where no reference to a basis, axes or components is made, implied or required, is adopted for the finite element formulation. Under this approach, the factorisation of the weighting function and also of the increment of the displacement field, can be performed by means of component-free operations avoiding both the use of any index notation and the subsequent reorganisation in matrix Voigt form. This new approach leads to a straightforward implementation of the formulation where only vectors and second order tensors in $${\mathbb {R}}^3$$ R 3 are required. The proposed formulation is as accurate as the standard Voigt based finite element method however is more efficient, concise, transparent and easy to implement.

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Section: Introductionmentioning

confidence: 99%

A component-free Lagrangian finite element formulation for large strain elastodynamics

et al. 2021

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“…An alternative to the proposed integration method would be to split the assembly of stiffness matrices into their in-plane and out-of-plane contributions as in [54], reducing the assembly cost significantly.…”

Section: Iga-galerkin Methods Strategymentioning

confidence: 99%

Efficient equilibrium-based stress recovery for isogeometric laminated curved structures

Patton¹,

Antolín²,

Kiendl³

et al. 2020

Preprint

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This work focuses on an efficient stress recovery procedure for laminated composite curved structures, which relies on Isogeometric Analysis (IGA) and equilibrium. Using a single element through the thickness in combination with a calibrated layerwise integration rule or a homogenized approach, the 3D solid isogeometric modeling grants an inexpensive and accurate approximation in terms of displacements (and their derivatives) and in-plane stresses, while through-the-thickness stress components are poorly approximated. Applying a further post-processing step, an accurate out-of-plane stress state is also recovered, even from a coarse displacement solution. This is based on a direct integration of the equilibrium equations in strong form, involving high order derivatives of the displacement field. Such a continuity requirement is fully granted by IGA shape function properties. The post-processing step is locally applied, which grants that no additional coupled terms appear in the equilibrium, allowing for a direct reconstruction without the need to further iterate to resolve the out-of-balance momentum equation. Several numerical results show the good performance of this approach particularly for composite stacks with significant radius-to-thickness ratio and number of plies. In particular, in the latter case, where a layerwise technique employing a number of degrees of freedom directly proportional to the number of plies would be much more computationally demanding, the proposed method can be regarded as a very appealing alternative choice.

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“…In this way, the time taken from design to analysis is reduced, resulting in dramatic efficiency gains. Currently, IGA has been applied successfully in numerous fields, such as solid mechanics [46][47][48] , heat transfer analysis [49][50][51] fluid mechanics [52][53][54] , fluid-structure interaction (FSI) simulations [55][56][57] etc. Up until now, research efforts have focused on establishing a practical framework for achieving the concept of 'design through analysis', but there are still no comprehensive studies of potential applications of computer-aided tolerancing (CAT).…”

Section: Introductionmentioning

confidence: 99%

Compliant assembly variation modeling for thin-walled structures considering clamping constraints and geometric deviations based on isogeometric analysis

Liu,

Li,

Liu

et al. 2024

Int J Adv Manuf Technol

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Geometric deviations and clamping constraints are the two major variation factors in thin-walled structure assembly processes. Geometric deviations are caused by inevitable uncertainties in manufacturing processes and have a significant impact on dimensional control for compliant assembly processes. Due to the flexibility of thin-walled structures, the clamping constraints during assembly greatly affect the compliant deformation of assembled structures. In this paper, a new method based on isogeometric analysis (IGA) considering geometric deviations and clamping constraints is proposed. The geometric deviations of thin-walled structures can be obtained by offsetting along the control points in an ideal part based on Nonuniform Rational B-Splines (NURBS), and the clamping constraints, such as fixture positioning deviations and connection matching deviations, are converted into displacement boundary conditions by the Lagrange multiplier method. Furthermore, the elastic force induced by initial geometric deviations is calculated using Kirchhoff-Love shell elements. Considering the coordination constraint relationship between shape closure and force closure in the compliant assembly process, a variation propagation model is developed using NURBS-based IGA. It integrates geometric deviations and compliant deformations into a unified mathematical representation framework by embedding exact geometry into assembly analysis. In addition, a numerical example is presented to demonstrate the accuracy and effectiveness of the developed method.

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Fast assembly of Galerkin matrices for 3D solid laminated composites using finite element and isogeometric discretizations

Cited by 7 publications

References 70 publications

A component-free Lagrangian finite element formulation for large strain elastodynamics

A component-free Lagrangian finite element formulation for large strain elastodynamics

Efficient equilibrium-based stress recovery for isogeometric laminated curved structures

Compliant assembly variation modeling for thin-walled structures considering clamping constraints and geometric deviations based on isogeometric analysis

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