A finite element large displacement analysis of stiffened plates

A finite element analysis of the large deflection behaviour of stiffened plates using the isoparametric quadratic stiffened plate bending element is presented. The evaluation of fundamental equations of the stiffened plates is based on Mindlin's hypothesis. The large deflection equations are based on von Kármán's theory. The solution algmrithm for the assembled nonlinear equilibrium equations is based on the Newton-Raphson iteration technique. Numerical solutions are presented for rectangular plates and skew stiffened plates.     

High-precision finite element analysis of cylindrical shells

This paper presents the finite element formulation to study the free vibration of cylindrical shells. The displacement function for the high-precision shell element with 16 degrees of freedom is approximated by a Hermitian polynomial of beam function type. The explicit formulation for the high-precision element is extremely efficient. For the purpose of comparison, the subject element is used to study the sample case of free vibration of a shell structure. The results are in good agreement with those published. The study shows that solution accuracy with fewer elements is assured and that accurate solutions are obtainable in the high-frequency range.     

Design and analysis of small submersible pressure hulls

Small submersibles, which permit man to observe and work as part of the three-dimensional undersea environment, are among the most promising tools for achieving effective exploitation of the oceans. An important element of any submersible is the pressure hull, frequently contributing one-fourth to one-half and more of the total vehicle weight. The Naval Ship Research and Development Center has played a major role in developing pressure hull structures for undersea vehicles. This paper describes some of the principal structural features of existing and envisioned small submersibles and summarizes recent advances in design and analysis methods. Particular emphasis is given to computer programs developed and/or used at the Center. Specifically, it describes advances in stress, stability, and vibration analyses as well as early stage developments in structural fatigue and reliability analyses. It also discusses computer programs and automated procedures designed for rapid response in feasibility studies and preliminary and final design cycles; these provide for both the generation of input data and the graphical display of computed results.     

Structural synthesis of frame reinforced,submersible, circular,cylindrical hulls

This paper describes a mathematical programming procedure for the automated optimal structural synthesis of frame stiffened, cylindrical shells. For a specified set of design parameters such as external pressure, shell radius and length and material properties, the method generates those values of the design variables that produce a minimum weight design. The skin, frame web and frame flange thicknesses and the flange width are treated as continuous variables. Frame spacing is considered a discrete variable. Constraint equations control local and general shell and frame instability and yield. Limits may be placed on the variable values, and certain geometric or space constraints can be applied. The mixed (continuous and discrete nonlinear programming problem is solved by a combination of a discrete ‘Golden Search’ for the optimal number of frames and the ‘Direct Search Design Algorithm’ which provides the optimum values of the continuous variables.     

Nonlinear finite element analysis of reinforced concrete stiffened and cellular slabs

A novel approach is presented in this paper for linear and nonlinear finite element analysis of reinforced and prestressed concrete cellular slabs based on a slab-beam model. Mindlin/Timoshenko assumptions are adopted in the slab-beam model which thus allows for transverse shear deformations. Several examples are presented to illustrate the accuracy and limitations of the method.     

A simple mixed finite element for static limit analysis

In this paper, we investigate the behavior of a simple mixed finite element for the limit analysis of plane structures. In particular, its ability to overcome incompressibility locking in plane strain situations is investigated. The element is constructed from a piecewise constant displacement field and a piecewise bilinear stress field, and is used within a mathematical programming based discrete representation of the classical static formulation. Several benchmark examples of both plane stress and plane strain situations are solved to illustrate the predictive accuracy and to assess the large-scale capability of the element. The results are compared with those obtained by a recent sophisticated enhanced strain mixed element formulation.     

A combined Rayleigh-Ritz/finite element method for the nonlinear analysis of stiffened plated structures

The paper describes a hybrid method for the non-linear analysis of steel plates and stiffened plating in which local (finite element) displacement functions are supplemented or replaced by global functions. The method is applied to the collapse analysis of box-girder bridges.     

Finite element analysis of stiffened plates

A finite element method is presented in which the constraint between stiffener and member is imposed by means of Lagrange multipliers. This is performed on the functional level, forming augmented variational principles. In order to simplify the initial development and implementation of the proposed method, two-dimensional stiffened beam finite elements are developed. Several such elements are formulated, each showing monotonic convergence in numerical tests. In the development of stiffened plate finite elements, the bending and membrane behaviors are treated seperately. For each, the stiffness matrix of a standard plate element is modified to account for an added beam element (representing the stiffener) and additional terms imposing the constraint between the two. The resulting stiffened plate element was implemented in the SAPIV finite element code. Exact solutions are not known for rib-reinforced plated structures, but results of numerical tests converge monotonically to a value in the vicinity of an approximate “smeared” series solution.     

Large deformation static and dynamic finite element analysis of extensible cables

Approximate numerical integration of the element total potential energy with polynomial interpolation of the displacements creates high order nonlinear, extensible, cable finite elements. Successful computations of static and dynamic large displacement cable problems are carried out with the element.     

Mixed least-squares finite element model for the static analysis of laminated composite plates

This paper presents a mixed finite element model for the static analysis of laminated composite plates. The formulation is based on the least-squares variational principle, which is an alternative approach to the mixed weak form finite element models. The mixed least-squares finite element model considers the first-order shear deformation theory with generalized displacements and stress resultants as independent variables. Specifically, the mixed model is developed using equal-order C⁰ Lagrange interpolation functions of high p-levels along with full integration. This mixed least-squares-based discrete model yields a symmetric and positive-definite system of algebraic equations. The predictive capability of the proposed model is demonstrated by numerical examples of the static analysis of four laminated composite plates, with different boundary conditions and various side-to-thickness ratios. Particularly, the mixed least-squares model with high-order interpolation functions is shown to be insensitive to shear-locking.     

Finite element buckling analysis of stiffened plates

An isoparametric stiffened plate bending element for the buckling analysis of stiffened plates has been presented. In the present approach, the stiffener can be positioned anywhere within the plate element and need not necessarily be placed on the nodal lines. The element, being isoparametric quadratic, can readily accommodate curved boundaries, laminated materials and transverse shear deformation. The formulation is applicable to thin as well as thick plates. The buckling loads for various rectangular and skew stiffened plates with varying skew angles and stiffness parameters have been indicated. The results show good agreement with those published.     

Finite element analysis of eccentrically stiffened plates in free vibration

A compound finite element model is developed to investigate eccentrically stiffened plates in free vibration. The plate elements and beam elements are treated as integral parts of a compound section, and not as independent bending components. The derivation is based on the assumptions of small deflection theory. In the orthogonally stiffened directions of the compound section, the neutral surfaces may not coincide. They lie between the middle surface of the plate and the centroidal axes of the stiffeners. The results of this study are compared with existing ones and with those of the orthotropic plate approximation. Modifications to the existing equivalent orthotropic rigidities are proposed.     

A static analysis of metal matrix composite spur gear by three-dimensional finite element method

A number of engineering components have recently been made using metal matrix composite (MMC) materials, due to their overwhelming advantages, such as light weight high strength, higher dimensional stability and minimal attack by environment, when compared with polymer-based composite materials, even though the cost of MMCs are very high. Power transmission gears are one such area able to make use of MMC materials. Here an attempt is made to study and compare the performance of gears made of MMC materials with that of conventional steel material gears. It may be concluded from this study that MMC materials are highly suitable for making gears that are to transmit even fairly large power.     

Finite element free vibration analysis of eccentrically stiffened plates

A new finite element model is proposed for free vibration analysis of eccentrically stiffened plates. The formulation allows the placement of any number of arbitrarily oriented stiffeners within a plate element without disturbing their individual properties. A plate-bending element consistent with the Reissner-Mindlin thick plate theory is employed to model the behaviour of the plating. A stiffener element, consistent with the plate element, is introduced to model the contributions of the stiffeners. The applied plate-bending and stiffener elements are based on mixed interpolation of tensorial components (MITC), to avoid spurious shear locking and to guarantee good convergence behaviour. Several numerical examples using both uniform and distorted meshes are given to demonstrate the excellent predictive capability of this approach.     

Finite element free vibration analysis of damped stiffened panels

Free vibration characleristics of a damped stiffened panel with applied viscoelastic damping on the flanges of the stiffeners are studied using finite element method. The complex nature of the rotational and transverse stiffnesses of the stringers is taken into consideration while deriving the stiffness and mass matrices of the damped stiffener element. The finite element method consists of representing the panel by rectangular plate elements of 12 d.o.f. and the stiffeners by beam elements of 8 d.o.f. which allow for bending, torsional and warping effects. Numerical results showing the effect of the geometric and material properties of the damping layer treatment on the resonant frequencies and loss factors of the composite panel are presented.     

High performance sparse static solver in finite element analyses with loop-unrolling

Symmetric positive definite equation solvers play a very important role in promoting the efficiency of the finite element analyses (FEA). The focus of this paper is to describe a new storage scheme—cell-sparse storage scheme—and the corresponding algorithm of the direct symmetric positive definite equation solver in FEA. Loop-unrolling (or simply unrolling) techniques are incorporated into sparse solvers to enhance the vector speed. Sparse storage schemes, out-of-core strategy, and numerical factorization are discussed. The performance in terms of elapsed time and memory requirement of different solvers are demonstrated by finding static displacement vectors for practical engineering problems. Numerical tests indicate that the cell-sparse storage scheme and the two-level unrolling can improve the performance of symmetric positive definite equation solvers significantly.     

Geometric nonlinear analysis of stiffened plates by the spline finite strip method

Geometric nonlinear analysis of stiffened plates is investigated by the spline finite strip method. von Karman’s nonlinear plate theory is adopted and the formulation is made in total Lagrangian coordinate system. The resulting nonlinear equations are solved by the Newton–Raphson iteration technique. To analyse plates having any arbitrary shapes, the whole plate is mapped into a square domain. The mapped domain is discretised into a number of strips. In this method, the displacement interpolation functions used are: the spline functions in the longitudinal direction of the strip and the finite element shape functions in the other direction. The stiffener is elegantly modelled so that it can be placed anywhere within the plate strip. The arbitrary orientation of the stiffener and its eccentricity are incorporated in the formulation. All these aspects have ultimately made the proposed approach a most versatile tool of analysis. Plates and stiffened plates are analysed and the results are presented along with those of other investigators for necessary comparison and discussion.     

Geometric uncertainties in finite element analysis

This paper demonstrates the use of automatic differentiation in solving finite element problems with random geometry. In the area of biomechanics, the shape and size of the domain is often known only approximately. Stochastic finite element analysis can be used to compute the variability in the structural response as a result of variability in the shape of the structural domain. Automatic differentiation can be used to compute the shape sensitivites accurately and effortlessly. Unlike randomness in material properties, the response variability can be the same as or greater than the variability in the input. When both the Young's modulus and geometry are random, it is likely that randomness in geometry will dominate randomness in Young's modulus.