New Straightforward Benchmark Solutions for Bending and Free Vibration of Clamped Anisotropic Rectangular Thin Plates

This study presents new straightforward benchmark solutions for bending and free vibration of clamped anisotropic rectangular thin plates by a double finite integral transform method. Being different from the previous studies that took pure trigonometric functions as the integral kernels, the exponential functions are adopted, and the unknowns to be determined are constituted after the integral transform, which overcomes the difficulty in solving the governing higher-order partial differential equations with odd derivatives with respect to both the in-plane coordinate variables, thus goes beyond the limit of conventional finite integral transforms that are only applicable to isotropic or orthotropic plates. The present study provides an easy-to-implement approach for similar complex problems, extending the scope of finite integral transforms with applications to plate problems. The validity of the method and accuracy of the new solutions that can serve as benchmarks are well confirmed by satisfactory comparison with the numerical solutions.

Three-Dimensional Bending Analysis of Multi-Layered Orthotropic Plates by Two-Dimensional Numerical Model

The paper presents effective numerical modelling of multi-layered plates with orthotropic properties. The method called the FEM23 is employed to construct the numerical model. The approach enables a full 3D analysis to be performed while using a 2D finite element mesh. The numerical model for a multi-layered plate is constructed by an assembling procedure, where each layer with orthotropic properties is added to the global numerical model. The paper demonstrates that the FEM23 method is very flexible in defining the multilayered plate, where the thickness of each layer as well as its mechanical orthotropic properties can be defined independently. Several examples of three-layered or nine-layered plates are analyzed in this paper. The results obtained by the FEM23 method coincide with the ones taken from the published papers or calculated with the standard 3D FEM approach. The orthotropic version of the FEM23 can be quite easily applied for other kinds of problems including thermo-mechanics, free vibrations, buckling analysis, or delamination.

Sound Enhancement of Orthotropic Sound Radiation Plates Using Line Loads and Considering Resonance Characteristics

A new vibro-acoustic method is presented to analyze the sound radiation behavior of orthotropic panel-form sound radiators using strip-type exciters to exert line loads to the panels for sound radiation. The simple first-order shear deformation theory together with the Ritz method is used to formulate the proposed method that makes the vibro-acoustic analysis of elastically restrained stiffened orthotropic plates more computationally efficient than the methods formulated on the basis of the other shear deformation theories. An elastically restrained orthotropic plate consisting of two parallel strip-type exciters was tested to measure the experimental sound pressure level curve for validating the effectiveness and accuracy of the proposed method. The resonance characteristics (natural frequency and mode shape) detrimental to sound radiation are identified in the vibro-acoustic analysis of the orthotropic plate. For any orthotropic sound radiation plate, based on the detrimental mode shapes, a practical procedure is presented to design the line load locations on the plate to suppress the major sound pressure level dips for enhancing the smoothness of the plate sound pressure level curve. For illustration, the sound radiation enhancement of orthotropic plates with different fiber orientations for aspect ratios equal to 3, 2, and 1 subjected to one or two line loads is conducted using the proposed procedure. The results for the cases with two line loads perpendicular to the fiber direction and located at the nodal lines of the major detrimental mode shape may find applications in designing orthotropic panel-form speakers with relatively smooth sound pressure level curves.

CONTACT PROBLEM FOR ORTHOTROPIC PLATES OF VARIABLE THICKNESS WITH A SPATIALLY INHOMOGENEOUS BASE

В работе приведено численное моделирование пространственной задачи контактного взаимодействия ортотропных плит переменной жесткости с упругими основаниями. Используемая методика расчета пригодна в случае любых известных контактных моделей упругих оснований. В качестве примера приведены численные результаты для пространственно-неоднородных оснований типа упругих слоев постоянной и переменной толщины. Система интегро-дифференциальных уравнений, к которой сводится задача, решается численно, сочетанием методов конечных разностей типа сквозного счета и граничных элементов. Найдены прогибы, изгибающие моменты и распределения контактных давлений прямоугольной плиты переменной жесткости, полностью примыкающей к основанию. Приводится анализ влияния на напряженно-деформированное состояние плиты, изменения ортотропных свойств ее материала и степень неравномерной сжимаемости толщи грунта. Разработанная методика позволяет эффективно моделировать работу плитных фундаментных конструкций, когда необходим учет неоднородности грунтов сжимаемой толщи в пределах габарита зданий или сооружений. The paper presents a numerical simulation of the spatial problem of contact interaction of orthotropic slabs of variable stiffness with elastic foundations. The calculation technique used is suitable for any known contact models of elastic foundations. As an example, numerical results are given for spatially inhomogeneous foundations such as elastic layers of constant and variable thickness. The system of integrodifferential equations, to which the problem is reduced, is solved numerically by a combination of finite difference methods such as end-to-end counting and boundary elements. Deflections, bending moments and contact pressure distributions of a rectangular slab of variable stiffness, completely adjacent to the base, are found. An analysis of the influence on the stress-strain state of the slab of changes in the orthotropic properties of its material and the degree of uneven compressibility of the soil thickness is given. The developed technique makes it possible to effectively simulate the operation of slab foundation structures when it is necessary to take into account the heterogeneity of the soil of the compressible strata within the dimensions of buildings or structures.

INVESTIGATION OF THE INFLUENCE OF AN INTERMEDIATE HINGE SUPPORT IN THE PROBLEM OF BENDING OF AN ELASTICALLY RESTRAINED ORTHOTROPIC BEAM

In this paper, based on the refined theory of orthotropic plates of variable thickness, a system of differential equations is obtained for solving the problem of bending of an elastically restrained beam with an intermediate condition. The beam thickness is constant and is subject to a uniformly distributed load. The effects of transverse shear are also taken into account. Passing to dimensionless quantities, an analytical closed solution is obtained. The question of the influence of changing the place of application of the intermediate condition on the solution is discussed. Depending on the location of the hinge bearing, the question of optimality was posed and resolved according to the principle of minimum maximum deflection. The results are presented in both tabular and graphical form. Based on the results obtained, appropriate conclusions are drawn.

Modified Reed Equation of Blast Load on Plate with Stiffener

The purpose of this study is to analyze numerically the effect of explosions on orthotropic slabs which have partial fixity placement and stiffeners in the x direction, namely in the short span direction. The modified blast load dynamic behavior is from Reed’s equation with 4th order polynomial on orthotropic plates with x-direction stiffener. The localized blast load centered in the middle of the strain, and the effects of thickness and stiffening on the vertical deflection of the plates are solved numerically using two auxiliary equations in the x and y-directions. It is found that there is vertical deflection with related to time.