The present paper is directed towards elasto‐plastic large deformation analysis of thin shells based on the concept of degenerated solids. The main aspect of the paper is the…
Abstract
The present paper is directed towards elasto‐plastic large deformation analysis of thin shells based on the concept of degenerated solids. The main aspect of the paper is the derivation of an efficient computational strategy placing emphasis on consistent elasto‐plastic tangent moduli and stress integration with the radial return method under the restriction of ‘zero normal stress condition’ in thickness direction. The advantageous performance of the standard Newton iteration using a consistent tangent stiffness matrix is compared to the classical scheme with an iteration matrix based on the infinitesimal elasto‐plastic constitutive tensor. Several numerical examples also demonstrate the effectiveness of the standard Newton iteration with respect to modified and quasi‐Newton methods like BFGS and others.
Nielen Stander, Anton Matzenmiller and Ekkehard Ramm
A critical assessment of the 4‐node assumed strain element as proposed by Dvorkin and Bathe is made. The element performed excellently in all investigated shell problems which…
Abstract
A critical assessment of the 4‐node assumed strain element as proposed by Dvorkin and Bathe is made. The element performed excellently in all investigated shell problems which sometimes caused difficulties for other assumed strain techniques. For efficient computation in the non‐linear range, linearization of the virtual work equation is done to yield the consistent tangent stiffness. The shell formulation is done for stress and strain tensors based on local element coordinates. To demonstrate the effectiveness and rapid convergence of the non‐linear formulation, three examples are tested for large displacements.
Mica Grujicic, S Ramaswami, Jennifer Snipes, Vasudeva Avuthu, Chian-Fong Yen and Bryan Cheeseman
Fiber-reinforced armor-grade polymer-matrix composite materials with a superior penetration resistance are traditionally developed using legacy knowledge and trial-and-error…
Abstract
Purpose
Fiber-reinforced armor-grade polymer-matrix composite materials with a superior penetration resistance are traditionally developed using legacy knowledge and trial-and-error empiricism. This approach is generally quite costly and time-consuming and, hence, new (faster and more economical) approaches are needed for the development of high-performance armor-grade composite materials. One of these new approaches is the so-called materials-by-design approach. Within this approach, extensive use is made of the computer-aided engineering (CAE) analyses and of the empirically/theoretically established functional relationships between an armor-grade composite-protected structure, the properties of the composite materials, material microstructure (as characterized at different length-scales) and the material/structure synthesis and fabrication processes. The paper aims to discuss these issues.
Design/methodology/approach
In the present work, a first step is made toward applying the materials-by-design approach to the development of the armor-grade composite materials and protective structures with superior ballistic-penetration resistance. Specifically, CAE analyses are utilized to establish functional relationships between the attributes/properties of the composite material and the penetration resistance of the associated protective structure, and to identify the combination of these properties which maximize the penetration resistance. In a follow-up paper, the materials-by-design approach will be extended to answer the questions such as what microstructural features the material must possess in order for the penetration resistance to be maximized and how such materials should be synthesized/processed.
Findings
The results obtained show that proper adjustment of the material properties results in significant improvements in the protective structure penetration resistance.
Originality/value
To the authors’ knowledge, the present work is the first reported attempt to apply the materials-by-design approach to armor-grade composite materials in order to help improve their ballistic-penetration resistance.
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Boštjan Brank and Adnan Ibrahimbegovic´
In this work we present interrelations between different finite rotation parametrizations for geometrically exact classical shell models (i.e. models without drilling rotation)…
Abstract
In this work we present interrelations between different finite rotation parametrizations for geometrically exact classical shell models (i.e. models without drilling rotation). In these kind of models the finite rotations are unrestricted in size but constrained in the 3‐d space. In the finite element approximation we use interpolation that restricts the treatment of rotations to the finite element nodes. Mutual relationships between different parametrizations are very clearly established and presented by informative commutative diagrams. The pluses and minuses of different parametrizations are discussed and the finite rotation terms arising in the linearization are given in their explicit forms.
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In this paper we derive a simple finite element formulation forgeometrical nonlinear shell structures. The formulation bases on a directintroduction of the isoparametric finite…
Abstract
In this paper we derive a simple finite element formulation for geometrical nonlinear shell structures. The formulation bases on a direct introduction of the isoparametric finite element formulation into the shell equations. The element allows the occurrence of finite rotations which are described by two independent angles. A layerwise linear elastic material model for composites has been chosen. A consistent linearization of all equations has been derived for the application of a pure Newton method in the nonlinear solution process. Thus a quadratic convergence behaviour can be achieved in the vicinity of the solution point. Examples show the applicability and effectivity of the developed element.
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Thomas Wright, Imran Hyder, Mitchell Daniels, David Kim and John P. Parmigiani
The purpose of this paper is to determine which of the ten material properties of the Hashin progressive damage model significantly affect the maximum load-carrying ability of…
Abstract
Purpose
The purpose of this paper is to determine which of the ten material properties of the Hashin progressive damage model significantly affect the maximum load-carrying ability of center-notched carbon fiber panels under in-plane tension and out-of-plane bending.
Design/methodology/approach
The approach used is to calculate the maximum load using a finite element model for a range of material property values as specified by a fraction factorial design. The finite element model used has been experimentally validated in prior work.
Findings
Results showed that for the laminates considered, at most three and as few as one of the ten Hashin material properties significantly affected the magnitude of the maximum load.
Practical implications
While the results of this paper only specifically apply to the laminates included in the study, the results suggest that, in general, only a small number of the Hashin material properties affect laminate load-carrying ability.
Originality/value
Knowing which properties are significant is of value in selecting materials to optimize performance and also in determining which properties need to be known to a high accuracy.
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J. Sorić, U. Montag and W.B. Krätzig
Presents a robust and unconditionally stable return‐mapping algorithm based on the discrete counterpart of the principle of maximum plastic dissipation. Develops the explicit…
Abstract
Presents a robust and unconditionally stable return‐mapping algorithm based on the discrete counterpart of the principle of maximum plastic dissipation. Develops the explicit expression for the consistent elasto‐plastic tangent modulus. All expressions are derived via tensor formulation showing the advantage over the classical matrix notation. The integration algorithm is implemented in the formulation of the four‐node isoparametric assumed‐strain finite‐rotation shell element employing the Mindlin‐Reissner‐type shell model. By applying the layered model, plastic zones can be displayed through the shell thickness. Material non‐linearity described by the von Mises yield criterion and isotropic hardening is combined with a geometrically non‐linear response assuming finite rotations. Numerical examples illustrate the efficiency of the present formulation in conjunction with the standard Newton iteration approach, in which no line search procedures are required. Demonstrates the excellent performance of the algorithm for large time respective load steps.
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Presents a range of numerical results obtained from the geometrically nonlinear analysis of a cantilevered cylindrical shell. Shows that, while the fine‐mesh solution involves no…
Abstract
Presents a range of numerical results obtained from the geometrically nonlinear analysis of a cantilevered cylindrical shell. Shows that, while the fine‐mesh solution involves no limit points, as the mesh is coarsened, an increasing series of “false limit points” is encountered.
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Implementation details of the assumed shear strain method in a novelfinite rotation shell theory are discussed. Careful considerations of thepertinent aspects of the Newton…
Abstract
Implementation details of the assumed shear strain method in a novel finite rotation shell theory are discussed. Careful considerations of the pertinent aspects of the Newton solution procedure are given. The latter results in a very robust performance of the presented 4–node shell element in some challenging finite rotation problems.
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The aim of this paper is to investigate the initiation and progress of damage in laminated composite shells at elevated moisture concentration and temperature due to low‐velocity…
Abstract
Purpose
The aim of this paper is to investigate the initiation and progress of damage in laminated composite shells at elevated moisture concentration and temperature due to low‐velocity impacts.
Design/methodology/approach
A finite element analysis procedure is developed to investigate the initiation and propagation of damage in laminated composite shells in hygrothermal environments.
Findings
It was found inter alia, that in the case of rise of temperature present FEM results match well with closed form solutions and that stress results at different levels of moisture concentration agree with the results published in the open literature.
Practical implications
The paper provides in‐depth insight into the progress of damage in laminated shell structures.
Originality/value
The paper investigates initiation and progress of damage in laminated composite shell structures due to low‐velocity impacts.