A new four‐node (non‐flat) general quadrilateral shell element for geometric and material non‐linear analysis is presented. The element is formulated using three‐dimensional continuum mechanics theory and it is applicable to the analysis of thin and thick shells. The formulation of the element and the solutions to various test and demonstrative example problems are presented and discussed.

http://web.mit.edu/kjb/www/Publications_Prior_to_1998/A_Continuum_Mechanics_Based_Four-Node_Shell_Element_for_General_Nonlinear_Analysis.pdf

A continuum mechanics based four‐node shell element for general non‐linear analysis

We briefly discuss the requirements on general shell elements for linear and nonlinear analysis in practical engineering environments, and present our approach to meet these needs. We summarize and give further insight into our formulation of a 4-node shell element using a mixed interpolation of tensorial components, and present a new 8-node element using this approach. Specific attention is given to the general applicability of the elements and their efficient use in practice.

/pdf/a-formulation-of-general-shell-elements-the-use-of-mixed-1j81jnzaqu.pdf

A formulation of general shell elements—the use of mixed interpolation of tensorial components†

Hourglass control in linear and nonlinear problems.

Hourglass control in linear and nonlinear problems

Local impact effects of hard missiles on concrete targets

A Simple and Efficient Approximation of Shells via Finite Quadrilateral Elements

Summary
A variation of the extended finite element method for three-dimensional fracture mechanics is proposed. It utilizes a novel form of enrichment and point-wise and integral matching of displacements of the standard and enriched elements in order to achieve higher accuracy, optimal convergence rates, and improved conditioning for two-dimensional and three-dimensional crack problems. A bespoke benchmark problem is introduced to determine the method's accuracy in the general three-dimensional case where it is demonstrated that the proposed approach improves the accuracy and reduces the number of iterations required for the iterative solution of the resulting system of equations by 40% for moderately refined meshes and topological enrichment. Moreover, when a fixed enrichment volume is used, the number of iterations required grows at a rate which is reduced by a factor of 2 compared with standard extended finite element method, diminishing the number of iterations by almost one order of magnitude. Copyright © 2015 John Wiley & Sons, Ltd.

/pdf/a-well-conditioned-and-optimally-convergent-xfem-for-3d-32b3kn7afe.pdf

A well-conditioned and optimally convergent XFEM for 3D linear elastic fracture

The present paper deals with the theoretical and numerical treatment of dynamic unilateral problems. The governing equations are formulated as an equivalent variational inequality expressing D' Alembert's principle in its inequality form. The discretization with respect to time and space leads to a static nonlinear programming problem which is solved by an appropriate algorithm. Some properties of dynamic unilateral problems are outlined and the influence of several parameters on the solution is investigated by means of numerical examples.

A linear finite element approach to the solution of the variational inequalities arising in contact problems of structural dynamics

KEYNOTE ADDRESSES Blast mitigation technologies: developments and numerical considerations for behavior assessment and design A geometric approach for dynamic buckling of autonomous lumped mass systems under impact. SECTION 1: STRUCTURES UNDER BLAST AND EXPLOSIVE SHOCK Risk analysis of industrial structures due to chemical explosions Shock wave load of window glass plate structure and hypothesis of its failure New architectural forms to reduce the effects of blast waves and fragments on structures Blast-resistant structural steel connections. SECTION 2: BURIED STRUCTURES UNDER EXPLOSIONS Trenching by explosives nearby an existing pipeline: charge size charts Strength analysis of buried pipes under explosive loads Determination of buried structure loads due to blast explosions. SECTION 3: STRUCTURAL CRASHWORTHINESS AND ENERGY ABSORBING SYSTEMS Reusable roadside impact attenuation devices Impact of ice loads on pile structures and deformation Effects of cutouts on static and dynamic behaviour of square aluminium extrusions Crushing of square aluminium extrusions with aluminium foam filler - numerical analyses The effect of induced imperfections on the formation of the first lobe of symmetric progressive buckling of thin-walled square tubes Crashworthiness of foam-cored sandwich panels with GRP inserts. SECTION 4: DYNAMIC BEHAVIOUR OF STRUCTURES Developments in the prediction of dynamic collapse Testing and analysis of elastic-plastic pinned beams under impulsive loading Stress wave effects on the dynamic axial buckling of cylindrical shells under impact Dynamic load factor in composite highway bridges Effects of bulk liquid on the dynamic characteristics of a thin walled cylindrical tank by finite element analysis and experimental modal analysis Numerical analysis of damped oscillations using modified finite integral method. SECTION 5: FULL AND SCALE-MODEL TESTING Testing and simulation of manufacture of metal machine components using exposive welding Development and applications of a new pulse pressure loading test rig Calibration of piezoelectric pressure and acceleration transducers Development of a test facility to simulate pyroshock environments in laboratory. SECTION 6: INTERACTION BETWEEN ANALYTICAL AND EXPERIMENTAL RESEARCH Target strength effects on the predicted threshold velocity for hemi- and ogival-nose penetrators perforating finite aluminium targets Vibrations of viscoplastic plates under impact load Investigation of the buckling of elastic composite rings under internal blast loading EBlast - an emergency blast system expert Orbital debris impacts against spacecraft multiple shields: comparison of hypervelocity experiments and hydrocode simulations Render-safe impact dynamics of the M557 fuze Blast and foreign object damage to plate structures using testing and simulations. SECTION 7: SEISMIC ENGINEERING APPLICATIONS Impact of neighbour building parts in case of earthquake Seismic response of two adjacent non-symmetric multistory buildings The seismic performance of precast columns using high strength concrete and post-inserted main reinforcement Calibration of a numerical model for the simulation of masonry under earthquake loading Extended and localized vibration modes of groups of modular buildings excited by ground motions or blasts. SECTION 8: MATERIAL RESPONSE TO HIGH RATE LOADING - 8.1 COMPOSITE LAMINATES Micromechanics based modeling of damage in composites under high velocity impact - a review Underwater shock wave loading on wood. 8.2 BRITTLE MATERIALS RESPONSE - Modeling of shock and impact behaviours of aluminium oxide A test for the rate effect on concrete fracture energy Effects of strain rate on concrete strength subjected to impact load - Dynamic compressive strength task by Split Hopkinson pressure bar method Dynamic strain softening of concrete in compression under rapid loading Hard impact testing of confined concrete cylinders Issues in the numerical simulation of strain-rate and pressure sensitive cementitious granular materials Advances for modelling of geological materials. 8.3 DEFORMATION AND FRACTURE UNDER IMPACT LOADING - Scaling issues in dynamic fragmentation Impact effect due to pavement irregularities on the dynamic response of bridges Testing with the torsional split Hopkinson bar at strain rates above 10,000 1/s The role of complex microstructures on high rate loading response On predicting and modelling material under impact loading On the use of the symmetric Taylor test to evaluate dynamic ductile compression fracture properties of metals Numerical simulation of composite structures under impact. 8.4 SHOCK WAVE PHENOMENA - ALEGRA - code validation: experiments and simulations Behaviour of a quartzite submitted to a spherical divergent shock-wave: experiments and modelling The influence of the crack tip plastic zone strain hardening on the metal High Cycle Fatigue behaviour A strain history dependent model for concrete High speed metal forming of circular disks and cylindrical tubes in a liquid shock tube. SECTION 9: BEHAVIOUR OF STEEL AND COMPOSITE STRUCTURES Ballistic impact on ceramic/composite armours An experimental set-up used in ballistic penetration The residual life of battle damaged bridges. SECTION 10: BEHAVIOUR OF CONCRETE MATERIAL AND STRUCTURES Testing and evaluation of out-of-plane strength of unreinforced masonry infills Dynamic behaviour of prestressed concrete beams under rapid speed loading 3D dynamic analysis and computer graphics application to impact failure simulation for reinforced concrete slabs Experimental studies on the inelastic behaviour of reinforced concrete panels under high-speed loading: effects of dynamic loading Experimental studies on the inelastic behaviour of reinforced concrete panels under high-speed loading: effects of rebar ratio and lap splices On the concrete material response to explosive loading - numerical simulations Validation of a viscodamage model for the dynamic behaviour of concrete Computed redial stresses in a concrete target penetrated by a steel projectile Modern geopenetrators and relevant revision of concrete penetration models Impulsive loading on reinforced concrete slabs - modelling considerations.

Structures Under Shock and Impact VI

Introduction Purpose and Scope. Mechanical Concepts and Mathematical Representations. Index Notation. Systems. Summation Convention. Position of Indices. Vector Notation. Kronecker Delta. Permutation Symbol. Symmetrical and Antisymmetrical Systems. Abbreviation for Partial Derivatives. Terminology. Specific Notations. Vectors, Tensors, and Curvilinear Coordinates Introduction. Curvilinear Coordinates, Base Vectors, and Metric Tensor. Products of Base Vectors. Components of Vectors. Surface and Volume Elements. Derivatives of Vectors. Tensors and Invariance. Associated Tensors. Covariant Derivative. Transformation from Cartesian to Curvilinear Coordinates. Integral Transformations. Deformation Concept of a Continuous Medium. Geometry of the Deformed Medium. Dilation of Volume and Surface. Vectors and Tensors Associated with the Deformed System. Nature of Motion in Small Regions. Strain. Transformation of Strain Components. Principal Strains. Maximum Shear Strain. Determination of Principal Strains and Principal Directions. Determination of Extremal Shear Strain. Engineering Strain Tensor. Strain Invariants and Volumetric Strain. Decomposition of Motion into Rotation and Deformation. Physical Components of the Engineering Strain. Strain-Displacement Relations. Compatibility of Strain Components. Rates and Increments of Strain and Rotation. Eulerian Strain Rate. Strain Deviator. Approximation of Small Strain. Approximations of Small Strain and Moderate Rotation. Approximations of Small Strain and Small Rotation. Stress Stress Vector. Couple Stress. Actions upon an Infinitesimal Element. Equations of Motion. Tensorial and Invariant Forms of Stress and Internal Work. Transformation of Stress-Physical Basis. Properties of a Stressed State. Hydrostatic Stress. Stress Deviator. Alternative Forms of the Equations of Motion. Significance of Small Strain. Approximation of Moderate Rotations. Approximations of Small Strains and Mall Rotations Linear Theory. Example: Buckling of a Beam. Behavior of Materials Introduction. General Considerations. Thermodynamic Principles. Excessive Entropy. Heat Flow. Entropy, Entropy Flux, and Entropy Production. Work of Internal Forces. Alternative Forms of the First and Second Laws. Saint-Venant's Principle. Observations of Simple Tests. Elasticity. Inelasticity. Linearly Elastic Material. Monotropic, Orthotropic, Transversely Isotropic , and Isotropic Hookean Material. Heat Conduction. Heat Conduction in the Hookean Material. Coefficients of Isotropic Elasticity. Alternative Forms of the Energy Potentials. Hookean Behavior in Plane-Stress and Plane-Strain. Justification of Saint-Venant's Principle. Yield Condition. Yield Condition for Isotropic Materials. Tresca Yield Condition. von Mises Yield Criterion. Plastic Behavior. Incremental Stress-Strain Relations. Geometrical Interpretation of the Flow Condition. Thermodynamic Interpretation. Tangent Modulus of Elasto-plastic Deformations. The Equations of Saint-Venant, Levy, Prandtl, and Reuss. Hencky Stress-Strain Relations. Plasticity without a Yield Condition Endochronic Theory. An Endochronic Form of Ideal Plasticity. Viscous Behavior. Newtonian Fluid. Linear Viscoelasticity. Isotropic Linear Viscoelasticity. Principles of Work and Energy Introduction. Historical Remarks. Terminology. Work, Kinetic Energy, and Fourier's Inequality. The Principle of Virtual Work. Conservative Forces and Potential Energy. Principle of Stationary Potential Energy. Complementary Energy. Principle of Minimum Potential Energy. Structural Stability. Stability at the Critical Load. Equilibrium States near the Critical Load. Effect of Small Imperfections upon the Buckling Load. Principle of Virtual Work Applied to a Continuous Body. Principle of Stationary Potential Applied to a Continuous Body. Generalization of the Principle of Stationary Potential. General Functional and Complementary Parts. Principle of Stationary Complementary Potential. Extremal Properties of the Complementary Potentials. Functionals and Stationary Theorem of Hellinger-Reissner. Functionals and Stationary Criteria for the Continuous Body Summary. Generalization of Castigliano's Theorem on Displacement. Variational Formulations of Inelasticity. Linear Theories of Isotropic Elasticity and Viscoelasticity Introduction. Uses and Limitations of the Linear Theories. Kinematic Equations of a Linear Theory. Linear Equations of Motion. Linear Elasticity. The Boundary-Value Problems of Linear Elasticity. Kinematic Formulation. Solutions via Displacements. Formulation in Terms of Stresses. Plane Strain and Plane Stress. Airy Stress Function. Stress Concentration at a Circular Hole in a Plate. General Solution by Complex Variables. Simple Bending of a Slender Rod. Torsion of a Cylindrical Bar. Linear Viscoelasticity. Kinematic Formulation. Quasistatic Problems and Separation of Variables. Quasistatic Problems in Terms of Displacements. Quasistatic Problems in Terms of Stresses. Laplace Transforms and Correspondence with Elastic Problems. Differential Geometry of a Surface Introduction. Base Vectors and Metric Tensors of the Surface. Products of the Base Vectors. Derivatives of the Base Vectors. Metric Tensor of the Three-Dimensional Space. Fundamental Forms. Curvature and Torsion. Volume and Area Differentials. Vectors, Derivatives, and Covariant Derivatives. Surface Tensors. Green's Theorem for a Surface. Equations of Gauss and Codazzi. Theory of Shells Introduction. Historical Perspective. The Essence of Shell Theory. Scope of the Current Treatment. Kinematics. Strains and Stresses. Equilibrium. Complementary Potentials. Physical Interpretations. Theory of Membranes. Approximations of Small Strain. The Meaning of Thin. Theory of Hookean Shells with Trnsverse Shear Strain. Theories under the Kirchhoff-Love Constraint Kinematics. Stresses and Strains. Equilibrium. Compatibility Equations, Stress Functions, and the Static-Geometric Analoty. Constitutive Equations of the Hookean Shell. Constitutive Equations of the Thin Hookean Shell. Intrinsic Kirchhoff-Love Theories. Plasticity of the Kirchhoff-Love Shell. Strain-Displacement Equations. Approximation of Small Strains and Moderate Rotations. Theory of Shallow Shells. Refinements-Limitations-References. Concepts of Approximation Introduction. Alternative Means of Approximation. Brief Retrospection. Concept of Finite Differences. Stationarity of Functionals Solutions and Forms of Approximation. Nodal Approximations via the Stationarity of a Functional. Higher-Order Approximations with Continuous Derivatives. Approximation by Finite Elements Physical and Mathematical Implications. Approximation via the Potential Convergence. Valid Approximations, Excessive Stiffness, and Some Cures. Approximation via the Modified Potential Convergence and Efficiency. Nonconforming Elements Approximations with Discontinuous Displcements. Finite Elements of Shells Basic Features. Supplementary Remarks on Elemental Approsimations. Approximation of Nonlinear Paths. References

Demosthenes Talaslidis

Papers

A Simple and Efficient Approximation of Shells via Finite Quadrilateral Elements

A well-conditioned and optimally convergent XFEM for 3D linear elastic fracture

A linear finite element approach to the solution of the variational inequalities arising in contact problems of structural dynamics

Structures Under Shock and Impact VI

Mechanics of Solids and Shells: Theories and Approximations