本文致力於改良Pagano方法，對四邊為簡支承、三維耦合的電磁彈多層疊合及功能性材料板，分別受到外力、電場及磁場的載重作用下進行分析。而沿厚度方向依冪級數律變分佈的功能性材料板，以往傳統Pagano方法顯得力有未逮。有別於Pagano方法，本文以混合型主變數理論推衍，取代傳統Pagano方法的位移主變數理論推衍，且將複數型的系統方程解，轉換成實數形式，並引入連續近似法、配合傳遞矩陣法，來進行功能性材料板的耦合分析。亦有探討功能性材料板受到外力、電場及磁場載重，與冪級數冪次所產生的相互關係。數值範例的結果顯示，改良Pagano方法，不僅計算效能高，與現有的三維精確解有相當一致的結果。

A modified Pagano’s classical method is developed for the three-dimensional (3D) coupled magneto-electro-elastic analysis of simply-supported, multilayered and functionally graded (FG) plates under a variety of magnetic, electric and mechanical loads. The material properties of FG plates are regarded as heterogeneous through the thickness coordinate and then specified to obey an identical power-law distribution of the volume fractions of the constituents. The present method differs from Pagano’s method in that a displacement-based formulation is replaced by a mixed formulation, the complex-values solutions of the system equations are replaced by the real-values solutions, a method of propagator matrix is newly-developed for the present modified Pagano’s method, and a successive approximation (SA) method is used to make the present modified Pagano’s method feasible for the coupled analysis of FG plates. In the illustrative examples, the influence of the power-law exponent on the magnetic, electric and mechanical variables induced in the FG plates is studied. The present modified Pagano’s method combined with the SA method is illustrated to be capable of efficiently approximating the available 3D solutions of FG plates to any desired accuracy.

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