Approximate Structural Analysis Research Articles

Predicted Thermal Stresses in a Trimaterial Assembly With Application to Silicon-Based Photovoltaic Module

Low-temperature thermally induced stresses in a trimaterial assembly subjected to the change in temperature are predicted based on an approximate structural analysis (strength-of-materials) analytical (“mathematical”) model. The addressed stresses include normal stresses acting in the cross-sections of the assembly components and determining their short- and long-term reliability, as well as the interfacial shearing and peeling stresses responsible for the adhesive and cohesive strength of the assembly. The model is applied to a preframed crystalline silicon photovoltaic module (PVM) assembly. It is concluded that the interfacial thermal stresses, and especially the peeling stresses, can be rather high, so that the structural integrity of the module could be compromised, unless appropriate design for reliability measures are taken. The developed model can be helpful in the stress analysis and physical (structural) design of the PVM and other trimaterial assemblies.

Analysis of interfacial thermal stresses in a trimaterial assembly

The interfacial stresses in, and the curvature of, an elongated trimaterial assembly, subjected to the change in temperature, are predicted based on an approximate structural analysis (strength-of-materials) model. The obtained results can be helpful in stress–strain evaluations and physical design of trimaterial assemblies in microelectronic and photonic packaging.

Development of the approximate analytical model for the stub-girder system using neural networks

This paper presents the methodology to develop a neural-networks-based model for approximate structural analysis. The approach is verified by modeling a stub-girder system to predict its behavior. The development of approximate analytical model by using neural networks is studied in an effort to find a method to efficiently generate credible outputs that are consistent with those by Vierendeel truss girder and finite element models. The criteria and rules for determining the neural network architecture are described using the performance evaluation with eight architecture design aspects and two subject variables to be compared. The criteria of accuracy are mostly focused because one of the objectives of an approximate analysis is to provide results that are within an allowable error.

Predicted thermal stresses in a bimaterial assembly adhesively bonded at the ends

The interfacial shearing and “peeling” stresses in an elongated bimaterial assembly, adhesively bonded at the ends and subjected to the change in temperature, are predicted, based on an approximate structural analysis (strength-of-materials) model. The stresses in the bonded joints due to the thermal expansion (contraction) mismatch of the adherend materials within the bonded areas (“local” mismatch), as well as the stresses, caused by the thermal mismatch of the adherend materials within the unbonded midportion of the assembly (“global” mismatch), are considered. The interaction of the “local” and the “global” stresses is evaluated and analyzed. It is shown that if the bonded joints are made long enough, the maximum stresses in the assembly will not be different from the stresses in an assembly with a continuous adhesive layer, no matter how long the unbonded midportion of the assembly might be. The obtained results can be helpful in the stress–strain evaluations and physical (mechanical) design of bimaterial assemblies in electronic and photonic packaging.

Modal Coupling and Accuracy of Modal Strain Energy Method

The modal strain energy (MSE) method is a technique for approximate analysis of structures whose models in the frequency domain show frequency-dependent stiffness and damping matrices such as structures containing viscoelastic dampers. In this paper, the concept of modal coupling in the frequency domain is addressed and expressions for diagonalizable frequency-dependent stiffness and damping matrices are given. The MSE method is described and the accuracy of this technique is investigated by computing the exact and approximate mean square responses of structures subjected to random excitation. Closed-form expressions of the mean square error are obtained for single–degree-of-freedom systems with linear hysteretic and Maxwell-type damping and the accuracy of the MSE method in the estimation of response of multi–degree-of-freedom structures with nonclassical, hysteretic, and Maxwell-type damping is investigated using a simple base-isolated model. Finally, the use of the MSE method for preliminary sizing of viscoelastic dampers is illustrated using a moment-resistant steel frame.

Approximate Structural Analysis of Circuit Card Systems Subjected to Torsion

Engineering analysis of module-populated printed circuit cards subjected to torsion is pursued by approximate engineering analysis, numerical (finite element), and experimental means. The engineering theory utilizes a simplified method of evaluating the torsional stiffness and maximum lead force, the latter found at the module corners. Finite element methods are used to check these values for circuit cards with a wide variety of module configurations, starting from a single-module to sixteen PLCC modules, having 44, 68, and 84 J-leads. An experimental torsion apparatus is used to obtain data for further comparison with the former approaches, and for getting data from the geometrically nonlinear (large deflection) range.

Arch shape optimization using force approximation methods

The objective of this paper is to provide a method of optimizing areas of the members as well as the shape of both two-hinged and fixed arches. The design process includes satisfaction of combined stress constraints under the assumption that the arch ribs can be approximated by a finite number of straight members. In order to reduce the number of detailed finite element analyses, the Force Approximization Method is used. A finite element analysis of the initial structure is performed and the gradients of the member end forces (axial, bending moment) are calculated with respect to the areas and nodal coordinates. The gradients are used to form an approximate structural analysis based on first order Taylor series expansions of the member end forces. Using move limits, a numerical optimizer minimizes the volume of the arch with information from the approximate structural analysis. Numerical examples are presented to demonstrate the efficiency and reliablity of the proposed method for shape optimization. It is shown that the number of finite element analysis is minimal and the procedure provides a highly efficient method of arch shape optimization.

Revised Method of Approximate Structural Analysis

A reliable and reasonably accurate approximate method of structural analysis for symmetric rectangular frames under symmetric vertical loadings is developed. For a fully loaded structure, the following set of assumptions gives acceptable results: (1) Girder inflection points exist at approximately 0.1L and 0.9L along each girder span; and (2) column inflection points exist at 0.33 I for first-story columns with fixed bases, 0.4H for top-story columns, and midheight of all remaining columns. For a checkerboard loading, the following set of assumptions is appropriate: (1) Girder inflection points exist at approximately 0.1L and 0.9L along each girder span; and (2) column inflection points exist at 0.33L for first-story columns with fixed bases, 0.2H for exterior columns that directly support a loaded girder, and at the bases of all remaining columns. Solutions from these two revised approximate methods are superior to solutions from a slightly different set of assumptions found in many contemporary structur...

Limitations of some of the approximate structural analysis methods that are used in structural system reliability

Structural system reliability often involves structures with non-linear behavior. In the reliability analysis, simplified structural models and simplified analysis procedures are used to model and analyze these structures. These simplified analysis procedures, for both frames and trusses, have their limitations. These limitations are illustrated in this paper through deterministic examples. It is recommended that further research be done on understanding the limitations of these methods and their effect on structural reliability analysis.

Potential Errors in Approximate Methods of Structural Analysis

A recurring procedural flaw exists in many textbook treatments of approximate methods for the analysis of rectangular, rigid frames under uniform vertical loading. The majority of textbooks surveyed cite an inappropriate assumption regarding the approximate analysis of vertically loaded frames which leads to erroneous solutions. One of the prevalent assumptions, which leads to incorrect shear forces and bending moments in columns, is that a negligible axial force exists in each girder. A more appropriate first-pass substitute might be to assume that inflection points occur in each column at mid-height, or at hinged supports of column bases at ground level. Using a simple, uniformly loaded, symmetric, rectangular frame as an example (this frame appears frequently in textbook examples), a trial revised set of assumptions produces an improved approximate solution. Work is proceeding to develop a fully tested, revised method of approximate structural analysis for vertically loaded rectangular frames.

Generalized age-adjusted effective modulus method for creep in composite beam structures. Part I — Theory

The age-adjusted effective modulus method for approximate analysis of structures exhibiting linear aging creep law and underlying Bažant's theorem is generalized to a form which is more accurate for composite beam structures in flexure. A rigorous derivation of a linear algebraic relationship between the internal force histories and the deformation histories of the beam is given using the integral operator symbolics.

Analysis and Computation of Energy Loss in Radial Tires

Abstract A comprehensive but simple analytical model for predicting the energy loss in radial tires is presented. Using approximate structural analysis, the model relates the basic material properties and construction variables of the tire to its energy loss or rolling resistance. The formulas developed were computer-programmed, and the tire rolling resistance and its distribution among the components of a typical radial automobile tire were computed. The significant contributions to rolling resistance were from tread compression, carcass cord extension and bending, and sidewall rubber bending. Parametric studies using the computer program were carried out to obtain the trends in rolling resistance due to changes in several tire material properties and construction variables. The computations also showed the existence of locally optimum values for the tread modulus, carcass cord modulus, and carcass cord end count which minimize the tire rolling resistance.

On the approximate analysis of structures composed of non-homogeneous linear visco-elastic material

A general method of analysis is presented for structures composed of non-homogeneous linear visco-elastic material and subjected to applied loads and displacements which are step functions of time. The procedure establishes the elastic and stationary-state response exactly and also furnishes a good approximation to the transient response. An application of the procedure to a problem of practical interest from the pressure vessel field concludes the paper.

Theoretical and experimental aerodynamics of the sailwing

The sailwing is a unique type of semiflexible foldable wing. A brief description of its construction, basic properties, and some past research, is used to introduce an analytical and experimental study of its aerodynamic characteristics. Emphasis is placed on an approximate structural analysis which treats the nonlinear behavior of the sail deflection. Twodimensional flexible airfoil theory and Prandtl lifting-line theory are used to establish the aerodynamic loading. The results allow prediction of the induced tensions, the nonlinear life curve, induced drag, and aeroelastic divergence of the sail chordwise deflection mode. Selected experimental results are presented for comparison with the theory, along with a brief discussion of the implications of the study regarding flight vehicle applications of the sailwing.

Elasticity equations for incompressible and nearly incompressible materials by a variational theorem.

A variational theorem is presented which is equivalent to the elastic field equations expressed in terms of the displacements and a function of the mean pressure. The variational theorem is particularly useful in the development of approximate structural analysis techniques for incompressible and nearly incompressible materials. An approximate analysis method derived by utilizing the Ritz technique in conjunction with the variational principle is illustrated. The results obtained from the application of this procedure to a sample problem are contrasted with those obtained by a similar technique that employs the theorem of minimum potential energy. The comparison illustrates that the results obtained from the analysis based upon the theorem of minimum potential energy becomes quite inaccurate for nearly incompressible materials whereas the solution technique based upon the new variational theorem yields accurate results.

The Plane Elastic Characteristics of Cord—Rubber Laminates

Results from an experimental study on rayon and nylon tire cords embedded in rubber are reported. Stress-strain curves in tension and compression on thick-walled cylinders of such materials show that much higher moduli of elasticity are exhibited by cords under tension than by cords in compression. However, the compression modulus of twisted cords is not insignificant, and such cords can apparently carry appreciable compressive loads when properly encased in rubber and when prevented from buckling. A bilinear approximation to the stress-strain curves of such materials is proposed as a means for approximate structural analysis of members utilizing these materials. Based on such a bilinear approximation, an analysis is presented for the state of stress and deformation in a laminated cord-rubber sheet under plane loads, using the principles of orthotropic materials. It is shown that four elastic constants are sufficient to describe the properties of a typical two-ply laminate when all cords are loaded in tension; a different set of four apply to the same body when it is loaded in such a way that the cords in both plies are in compression. The existence of interply stresses between lamina in built-up cord-rubber sheets is shown, and expressions are derived for the magnitude of such stresses as functions of the externally applied forces. Two different types of interply stresses are identified. Experiments were performed using laminated cord-rubber cylinders under various stress states in order to compare various moduli of elasticity with those predicted from theory. Such comparisons seem to indicate that the theories proposed adequately describe the composite materials being considered. It may generally be concluded from the work reported here that the elastic properties of any type of cord-rubber laminate may be derived from the elastic properties of a single sheet of its constituent material.

Approximate analysis of structures in the presence of moderately large creep deformations

Approximate analysis of structures in the presence of moderately large creep deformations