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A new consistent corotational formulation for nonlinear dynamics of beams with arbitrary thin-walled cross-section is presented. The novelty is that the warping deformations and the eccentricity of the shear center are fully taken into account. Therefore, additional terms are introduced in the expressions of the inertia force vector and the tangent dynamic matrix. Their contribution is then investigated considering several numerical examples. Besides, the element has seven degrees of freedom at each node and cubic shape functions are used to interpolate local transverse displacements and axial rotations. The formulation's accuracy is assessed considering five examples with comparisons against 3D-solid solutions.

A 6-node triangular Reissner-Mindlin plate element with eXtended Finite Element Method (XFEM) formulation for yield line analyses is presented. The XFEM formulation with regularized enrichment is employed to reproduce a displacement field with a locally high gradient in the vicinity of a yield line in plate structures. The MITC technique is employed to mitigate shear locking in both the smooth and the locally non-smooth displacement fields. Several numerical examples are presented to illustrate the effectiveness of the XFEM enrichment in yield line analysis as well as the necessity and the effectiveness of the MITC technique in shear locking alleviation in the XFEM formulation. Accepted version

A four node, displacement based, acoustic element is developed. In order to avoid spurious rotational modes, a higher order stiffness is introduced. The higher order stiffness is developed from an incompatible strain field which computes element volume changes under nodal rotational displacements fields. The higher order strain satisfies the IET requirements, non affecting convergence. The higher order stiffness is modulated, element by element, with a factor. Thus, the displacement based formulation is capable of placing the spurious rotational modes over the range of physical compressional modes that can be accurately captured by the mesh.

This paper studies the propagation of plane harmonic waves in unbounded media discretized by the standard six-node triangular finite element. The element stiffness matrix is split into basic and higher order components which are obtained from mean and deviatoric strain fields, respectively. This decomposition is applied to the elastic energy. Based on the properties of the higher order energy, two values of the wave number are selected. Depending on the desired precision one of those values can be used as optimum cutoff wave number to properly capture a wave field.

We present in this paper a shell element that models the three-dimensional (3D) effects of surface tractions, like needed when a shell is confined between other solid media. The element is the widely used MITC4 shell element enriched by the use of a fully 3D stress-strain description, appropriate through-the-thickness displacements to model surface tractions, and pressure degrees of freedom for incompressible analyses. The element formulation avoids instabilities and ill-conditioning. Various example solutions are presented to illustrate the capabilities of the element.

This paper studies the propagation of plane harmonic waves in plane-strain solids discretized by the standard eight-node quadrilateral finite element. This element is formulated in energy-orthogonal form. It means that the stiffness matrix is split into basic and higher order components which are obtained from the mean and deviatoric strain fields, respectively. The major subject is to obtain reference values for the wave number that can be used as optimum cutoff wave number to properly capture a wave field. The procedure is based on the properties of the higher order elastic energy.

When a plate travels at a high speed, gyroscopic and in-plane forces affect the dynamic behavior of the plate. The formulation of a traveling triangular plate element subjected to in-plane forces and gyroscopic forces is presented in this paper. This moving element is developed by modifying a discrete Kirchhoff theory element. The element matrices are derived and expressed explicitly. To verify the formulation and the program, five cases of an axially traveling rectangular plate subjected to distributed in-plane forces are studied. The results show that this moving triangular plate element (moving discrete Kirchhoff theory) provides an alternate technique for modeling an axially traveling plate subjected to in-plane forces.

An approach for adding drilling rotations to the constant strain triangle, such that the added rotation stiffness contributes a minimum to the strain energy of the triangle is presented. The element is combined with a bending triangle to produce a flat shell element having six-degrees-of-freedom per node. Allman’s triangle with true drilling rotations is also combined with the same bending element. These two facet shell elements are examined for their capacity to accurately simulate inextensional bending of general thin shells. A novel eigenvalue procedure and specially designed inextensional bending patch tests for thin shells are applied. Selected practical thin shell problems are also solved.

We use the Papcovitch–Neuber (PN) solution to the Navier equation and develop a new 14-node brick element PN5X1, to represent linear stress fields exactly. We perform patch tests, to assess its ability to converge in plate and shell problems. We also test the new element in rectangular and circular plates with simply supported and clamped edges and subject them to point and uniformly distributed loads. We also use it in locking tests and in low-energy deformation mode tests of rectangular plates. PN5X1 passes the patch tests and predicts, in the limit of discretization, theoretical values in almost all the plate and shell problems.

This paper deals with buckling and free vibrations of multilaminated structures of arbitrary geometry and lay-up using a single layer higher order shear deformation theory discrete model. This model is based on an eight-node C0 serendipity finite element with 10 degrees of freedom per node to contemplate general applications. The present model is tested on the evaluation of buckling loads and free vibrations of multilaminated plates and shells. The effects of different number of layers, lamination angles, material anisotropy, and length or radius to thickness ratios are studied.

In this paper a new method for crack identification in beams is presented. The transverse surface crack is considered to remain always open. Using this method the crack location and depth can be determined. The method is based on the basic observation that the eigenmodes of any cracked structure are different from those of the uncracked one. The differences are due to the slope discontinuity of the vibration eigenmodes at the crack location. The basic idea in this paper is to correlate the mode differences with the crack depth and location. These correlated differences are chosen to be (a) the ratio of two amplitude measurements in two positions and (b) the distance of the node of the vibrating mode from the left end, while the structure is vibrating under harmonic excitation in resonant condition. The analytical results presented here are also experimentally proven. In a free-free beam the two first eigenmodes are measured and the node distance of the uncracked and the cracked beam are used in pre-plotted diagrams to verify the crack location and depth. Here, it is also theoretically proved that the above results for the beam are the same in both the air and the water. This is valid irrespective of whether the damping effect is taken into consideration or not.

Natural frequencies of cylindrical shells with a circular plate attached at arbitrary locations are determined for various boundary conditions and L/D ratios. The semi-analytical finite element method is used for the analysis. A conical shell element with four degrees of freedom per node and two nodes per element is used. For clamped-clamped and simply-supported boundary conditions the plate is attached at the center of the shell. For a clamped-free boundary condition the plate is at the free end of the shell. The effects of plate thickness and L/D ratio of the shell on the frequencies of the shell-plate combination are investigated. Copyright ? 1996 Elsevier Science Ltd.

In this paper a new method for the determination of the depth and the location of a transverse surface crack in a beam is presented. Simulating the crack by a local compliance matrix of six degrees of freedom has been used for crack modelling in the last decade. This matrix contains diagonal and non-diagonal terms, and thus coupling among different modes of vibration occurs. A harmonic force or a moment of known amplitude and frequency is used to dynamically excite the beam. The exciting frequency should be far from a system eigenvalue to avoid the effect of the damping near resonance. Two response measurements at a point are required by the method. The first measurement is taken in the direction of the excitation, while the second one in the direction where coupling effect occurs due to the crack. The crack is considered to always remain open. The identification of the existence of the crack will be shown to be feasible, if a response on a degree of freedom, other than the one of the excitation, exists. A Timoshenko beam finite element of six degrees of freedom per node, is used. This method can be applied in structures in air as well as under water.

A new four-node quadrilateral plate bending element is presented for the analysis of thin and moderately thick plates of general plan form. The element has three degrees of freedom at the corners. Numerical experiments are given and they indicate that the element does not ‘lock’ for thin plates and gives excellent results for both thin and moderately thick plates.

This paper presents a nine-node three-dimensional curved shell finite element formulation for linear steady-state heat conduction in laminated composites where the temperature approximation for the laminate is piecewise hierarchical and is derived based on the P-version. The temperature approximation for the element is developed by first establishing a hierarchical temperature approximation for each lamina of the laminate and then by imposing inter-lamina continuity conditions of temperature at the interface between the laminas. The approximation functions and the nodal variables for a lamina are derived directly from the Lagrange family of interpolation functions of order pξ, pη and kPζ. This is accomplished by first establishing one-dimensional hierarchical approximation functions and the corresponding nodal variable operators in the ξ, η and kζ directions for the equivalent (3, 3 and 1 node) configurations that correspond to pξ + 1, pη + 1 and kpζ + 1 equally spaced nodes in the ξ, η, and kζ directions and then taking their products. The nodal variables for the laminated shell element are derived from the nodal variables of the laminas and the inter-lamina continuity conditions of temperature. The element formulation ensures C0 continuity of temperature across inter-element as well as the inter-lamina boundaries.

This study shows that the common practice in existing frame methods of assuming the rotations of the coupling beams at beam-wall joints to be equal to the rotations of the horizontal rigid arms would lead to incompatibility between the beam and wall elements at their joints and eventually errors in the effective stiffness of the coupling beams. It is postulated that to resolve the problem, the rotational DOF at the beam-wall joints should be changed to the rotations of the vertical fibres there. This would, however, necessitate the use of frame elements with two rotational DOF at each end or solid wall elements with rotational DOF at each node to model the structure. Such required frame and solid wall elements are developed in this paper based on a Timoshenko beam element with two rotational DOF at each end. The resulting new frame method is much more accurate and versatile than the existing frame methods.

A standard four-noded rectangular element with seven degrees of freedom at each node is developed for the analysis of flexible laminated plate structures having a constant thickness of any individual layer. The displacement model is so chosen that it can explain adequately the parabolic distribution of transverse shear stresses and the non-linearity of in-plane displacements across the thickness. A wide range of plates, thick to thin and semi-rigid to flexible, are examined for different loadings and boundary conditions. The results are compared with the existing analytical and numerical solutions. The present element formulation confirms its applicability for a wide variety of laminated composite plates.

In this paper, a three-dimensional model for dynamic response analysis of jacket-type offshore platforms under random sea waves is established. The sea waves are considered to be zero mean, stationary and ergodic Gaussian random processes specified by the P-M wave height spectrum. Linear wave theory and the generalized Morrison equation are used to calculate the wave forces on the structure. The fluid-structure interaction and the couplings of the motion in different directions at each node are considered. The fluid drag forces are linearized by stochastic linearization techniques. The mean-square responses are obtained by Gauss-Legendre numerical integration. Numerical results for a platform with a height of 65 m to symmetrical and unsymmetrical loads are presented and contrast with the corresponding results of one- and two-dimensional models. Some more detail and practical description, such as the response in the vertical direction and the unsymmetrically loaded behaviour, are given.

In this note, it is shown that the rotational degrees of freedom at a node of a spatial finite beam element are the components of a vector regardless of their magnitudes, as long as the structure to be analysed is composed of slender beams, and what may prevent them from being considered as the components of a vector is the presence of significant transverse shear strains, which usually appear in short beams, rather than the magnitudes of the rotations.

A finite element method is developed for the computation of elastodynamic stress intensity factors at a rapidly moving crack tip. The method is restricted to bodies whose surfaces and two-material interfaces are either parallel to the direction of propagation or are sufficiently remote. The crack tip starts to move at the instant that it is struck by an incident wave. The finite element grid moves undeformed with the crack tip. The main result consists in the fact that the method of non-singular calibrated crack tip elements, in which the stress-intensity factor is determined from its statically calibrated ratio to the crack opening displacement in an adjacent node, is extended to dynamic problems with moving cracks, for both in-plane and anti-plane motions. The dependence of the calibration ratio on the crack tip velocity is established from previously developed analytical solutions for the near-tip displacement fields. Numerical results compare favorably with known analytical solutions for cracks moving in an infinite solid. The grid motion causes an apparent asymmetric additional damping matrix.

A numerical model is derived for the plane-stress elastic deformation of two concentric hollow cylinders with acircular contact surfaces. Given the detailed undeformed section geometry, the model computes the circumferential distributions of interfacial pressure and gap, and the distortion of the two free surfaces. The interface is partitioned into axial strip elements with radial displacement nodes at their boundaries and a piecewise linear pressure distribution from node to node. Influence coefficients linearly relating nodal displacements to nodal pressures are computed using a finite Fourier series expansion of the pressure distribution in conjuction with exact expressions for the deformation of a sinusoidally loaded thick ring. The iterative solution of the nonlinear system of node equations entails computing the currently nonzero nodal pressures by matrix inversion and then updating the contact/gap configuration. The model is demonstrated for a 400 node, multiple-contact interface between a machined shaft and sleeve with measured acircularity profiles.

The finite element method is applied to obtain inplane stresses in a rotating disc with dissimilar holes near its periphery. Twelve node isoparametric elements with cubic displacement function are used to idealise the disc portion under study. Plane stress conditions of linear elasticity are considered. The stress concentration which is prevalent at the contours of the holes is estimated in the form of factor. The results for an example problem are compared with those from analytical solutions for a similar problem in continuum mechanics. Thermal stresses can also be obtained for a given temperature distribution with the same element and idealisation of disc portion.

A doubly curved isoparametric triangular shell element with six nodes is developed by numerical integration. Quadratic interpolation is applied to freedoms u, v, w, ∂w/∂x and ∂w/∂y at each node so that the element has a total of 30 freedoms. The element is an extension of the “thick slab” element derived by Mohr[1] using the natural strain technique developed by Argyris and Scharpf. Numerical experiments are conducted with this plate bending element to show that it gives satisfactory results for very thin plates. Next the element is augmented by the appropriate in-plane freedoms and applied to several thin shell analyses and found to give good results. From these preliminary results this economical shell element appears a promising means of analysis of thin and thick shell structures.

A new finite element for modeling fiber-reinforced composite plates and shells is developed and its performance for static linear problems is evaluated. The element is a nine-node degenerate solid shell element based on a modified Hellinger-Reissner principle with independent inplane and transverse shear strains. Several numerical examples are solved and the solutions are compared with other available finite solutions and with classical lamination theory. The results show that the present element yields accurate solutions for the test problems presented. Convergence characteristics are good, and the solution is relatively insensitive in element distortion. The element is also shown to be free of locking even for thin laminates.

Numerical results show that the transverse shears are free of oscillation for regular or quasi-regular meshes of four-node plate elements based on Mindlin-Reissner theory. However, even small perturbations of these meshes can introduce severe oscillations throughout the mesh. These findings apply to the underintegrated elements with and without stabilization and to the fully integrated elements which use assumed shear strains. A filtering procedure capable of recovering improved shears is presented.

A nine-node element, designated as SHEL9, has been developed for analysis of thin plates and shells. The element formulation is based on the degenerate solid shell concept and a modified Hellinger-Reissner principle with independent in-plane and transverse shear strains. Numerical tests indicate that the present SHEL9 element with uniform 3 × 3 point integration rule is free of locking, and it gives reliable solutions even for thin plates and shells.

Distorted, nine-noded, Lagrangian, isoparametric elements are studied to determine if stress intensity factors can be calculated more accurately with these elements than with eight-noded quarter-point elements. To achieve square-root singular stress behavior in the nine-noded element, the mid-side nodes adjacent to the crack tip are moved to the quarter-point and the nodal point within the element is positioned along the element diagonal, at least at the quarter-point. Several optimal positions for this node are determined. Through two numerical examples, it is seen that the eight-noded element performs nearly as well, and sometimes better than the nine-noded element.

Near the fixed end boundaries of cantilever swept plates, a high stress variation, especially in a near13; singular fashion at the re-entrant corner, requires that at least at this region, one requires an analysis with a high13; precision triangular plate bending element. An idealisation of an entire swept plate, especially one of large aspect13; ratio, by high precision elements may be uneconomical and the approximation of regions away from the boundary13; by a suitable beam element will achieve a considerable reduction in problem size. Thus one can achieve a structural13; reduction of the swept plate problem by the use of plate elements in regions of high stress variation, beam elements13; in regions away from the kinematically constrained boundaries and a variationally condensed transition plate/beam13; element which will have the nodes and degrees of freedom of high precision CI continuous plate elements along13; one boundary and the node and degrees of freedom of a beam element along the other boundary. This interphase13; element will provide the required transition from thin plate to thin beam behaviour. In this paper, extensive results13; indicate a considerable reduction in nroblem size and solution time without significant loss of accuracy in stresses.13; displacements and slopes.