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For Mechanics of Materials Subject (Mms) Emirates Journal for Engineering Research, 13 (2), 73-78 (2008) (Regular Paper) ANALOGY BASED LEARNING (ABL) FOR MECHANICS OF MATERIALS SUBJECT (MMS) M. Isreb School of Applied Sciences and Engineering, Monash University Gippsland Campus Northways Road, Churchill, Victoria 3842, Australia Email: [email protected] (Received May 2008 and accepted August 2008) ﻻ يوجد دليل في المراجع واﻷبحاث المنشورة على استخدام التعليم بواسطة النمذجة للعنصر الرياضي في مادة الھندسة الميكانيكية للمواد المتشكلة (والمعروفة أيضاً في أوساط معملي الھندسة باسم ميكانيكا المواد (MMS)). ويھدف تطبيق التعليم بواسطة النمذجة المقدم في ھذه الورقة إلى محاولة تسھيل استيعاب الطﻻب لتلك المادة الصعبة. وقد تم استخدام الطريقة القياسية لنمذجة العزوم باسلوب مبتكر. وقد اختبر الباحث ھذه الطريقة لمدة عشرين عاماً في جامعة موناش باستراليا. وأثبتت الطريقة نجاحھا بغض النظر عن طريقة الطﻻب وقدرتھم على التحصيل طبقاً ﻻمكانياتھم العقلية. وتميزت الطريقة بقابلية التطوير والمرونة. There is no evidence in the literature of using Analogy based-learning (ABL) education for the mathematics components of Engineering Mechanics of Deformable Bodies subject (also known widely amongst engineering educators by the name Mechanics of Materials subject, abbreviated as MMS). The motive of using the ABL for MMS in the present paper is to attempt to make, such already difficult subject, easy one to get across to students. The method used in the paper is based on standard ABL methodology of coupling, in an innovative way, each ABL source with an ABL target of the MMS. The author has tested the new approach for two decades at Monash University, Australia. The approach has proved to bring the students potentials to its fullest regardless of their style of learning, within the eight brain sectors. The approach has proved both feasible and extensible. Keywords: Analogy-Based Leaning (ABL), Mechanics of Materials Subject (MMS), Innovative Learning. 1. INTRODUCTION learning (PjBL) in MMS is another extension of PBL. It is the MMS type of project work which can mimic Mechanics of Materials subject (MMS), also some professional reality, taking from one class session to educators call it Engineering Mechanics of several weeks to complete, Perrenet et al.[3]. Inquiry- Deformable Bodies subject is concerned with the based learning (IBL) in MMS is a flexible holistic mathematical formulations of stresses and adaptation of PBL, which can be seen as any deformations for engineering deformable bodies. pedagogy that poses a problem or investigation first, MMS is the core engineering subject for almost all and subsumes other instruction under the pursuit of the engineering disciplines. Mathematically speaking, quest, Edelson et al.[4]. MMS is one of the most difficult core engineering Learning by analogy in MMS is the central theme subjects. It contains heavy dose of mathematical of the paper keeping in mind that ABL could be used derivations of stresses and deformations leading to its with PBL, PjBL, and IBL as shown in Figure 1. constitutive laws and their related boundary conditions Learning by analogy typically involves finding a set of and other related problems. systematic correspondences (a mapping) between a Numerous attempts have been detected in literature better-known source analogy and a more novel target. to make such difficult subject easy to get across to In the present paper, the word analogy in Analogy- students using well known learning approaches, but based learning (ABL) of MMS refers to the relation none of such approaches utilises learning by analogy. between the source and the target themselves, e.g. the Problem-based learning (PBL) in MMS is one of such definition of Wikipedia Encyclopedia[5]. It should be approaches already used in which the MMS’ problems noted that it is the first time in literature an ABL is drive the learning. That is, before students learn some specifically applied it to the mathematics of MMS. knowledge in MMS they are given a problem. The Furthermore, the paper introduces an innovative problem is posed so that the students discover that educational tool to facilitate learning of MMS by they need to learn some new knowledge before they [1] [2] incorporating major mechanics constitutive laws into can solve the problem. Goulet and Margetson specially developed analogical relations between the show some of the challenges in PBL. Project-based sources and the targets of MMS mathematics. 73 M. Isreb Table 1. Sample topics of a typical MMS syllabus No. Topic Description PBL PjBL (Problem-based (Problem-based 1 TENSION, COMPRESSION, AND SHEAR learning) learning) Introduction to MMS / Normal Stress and Strain / Mechanical ABL in MMS Properties of Materials / Elasticity, Plasticity, and Creep / Linear Elasticity, Hooke's Laws, and Poisson's Ratio / Shear Stress and (Analogy based Strain / Allowable Stresses and Allowable Loads. Changes in learning in Mechanics Lengths of Axially Loaded Members (Axial Deformation) / Changes of Materials Subject) in Lengths of Non-uniform Bars 2 TORSION Introduction / Torsional Deformations of a Circular Bar / Circular Bars of Linearly Elastic Materials / Non-uniform Torsion / Stresses and Strains in Pure Shear IBL 3 STRESSES IN BEAMS (Inquiry-based Introduction / Pure Bending and Non-uniform Bending / Curvature of learning) a Beam / Longitudinal Strains in Beams/ Normal Stresses in Beams (Linearly Elastic Materials) / Shear Stresses in Beams 4 DEFLECTIONS OF BEAMS Introduction / Differential Equations of the Deflection Curve / Figure 1. Relationships between ABL, PBL, PjBL and IBL. Deflections by Integration of the Bending-Moment Equation / Deflections by Integration of the Shear-Force and Load Equations / The ABL of MMS is introduced in the present Method of Superposition papers to engineering and sciences students by means of handy tables especially tailored for flexible ABL Table 2. ABL source-target notations for Hooke’s laws within topic 1 delivery by science and engineering faculties. The of table 1 rational behind such development is the following: ABL SOURCE ABL TARGET The MMS as a subject has always been perceived by Axial Loading Shear Loading students to be a very difficult (i.e. mathematically) Symbol Meaning of Rhyming-analogy Meaning of Rhyming- Symbols Symbol analogy Symbol oriented subject to learn. Consequently, one can σ Normal stress τ Shear stress clearly see the need for an appropriate methodology in E Modulus of G Modulus of elasticity in relation to developing an innovative and educationally elasticity shear simplified ABL mathematical approach for MMS. The ε Normal strain γ Shear strain methodology of the paper is discussed next. Table 3. ABL source-target for Hooke’s laws within topic 1 of table 1 2. METHODOLOGY as per the analogical notations of table 2 ABL SOURCE ABL TARGET The paper’s methodology of ABL for MMS is Axial Loading Shear Loading summarised in the following three parts: Part (a) σ = Eε Hook’s Law τ = Gγ Hook’s Law in shear introduces ABL for MMS framework: i.e. formulates, implements and identifies the differences between ABL and the classical/conventional teaching of MMS; Part (b) of step 1, of the paper’s methodology, is Part (b) presents examples of ABL for MMS in support best explained through an example. The example is of (as well as to illustrate) the methodology used; and shown in Table 1. The Table shows sample topics of a Part (c) shows the reasoning of the ABL methodology typical MMS syllabus. This is a conventional /classical approach. MMS teaching which involves the teaching of one Part (a) of the paper’s methodology consists of the topic after another (sequentially) with no regard to their following three steps: Step 1, as a standalone step, analogical mathematical connections at all (i.e. no represents nothing but the classical (conventional) regards to analogical relations between the sources and approach to MMS teaching; while steps 2 and 3 are the the targets of MMS mathematics). actual analogical steps within the three-step procedure Step 2 of part (a) of the paper’s methodology calls on of part (a). the lecturer to identify and teach the analogy based Step 1, of part (a) of the methodology, calls for the mathematical elements within the components of the lecturer to teach the MMS selected topics as in a topic at hand while the topic is being taught (e.g. classical way, i.e. as described in the syllabus of the analogy within topic i, analogy within topic j, analogy subject (e.g. teach topic i, then teach topic j, then topic within topic k etc). Part (b) of step 2, of the paper’s k etc.). A typical MMS syllabus of the subject can be methodology, is best explained through the following found in many textbooks, e.g. Gere[6]. The author of three example: the present paper had the privilege of reviewing Gere[6] - Example One: Table 2 is the first example of by invitation, as acknowledged on page Xiii. It should step 2 of ABL framework. Specifically it is be noted that the author of the present paper restricted about the ABL source-target notations for his revision of Gere[6] to step 1of part (a) of the paper’s Hooke’s Laws within topic 1 of Table 1. ABL methodology. source is the axial type of loading and ABL target is the shear type of loading. 74 Emirates Journal for Engineering Research, Vol. 13, No.2, 2008 Analogy Based Learning (ABI) for Mechanics of Materials Subject (MMS) Table 4. ABL source-target notations for boundary conditions’ mathematical equivalency within topic 4 of table 1 ABL SOURCE ABL TARGET Symbol Meaning Equivalence Equation’s Order (of differentiation) Symbol Meaning Equivalence Equation v Deflection v = v Deflection ( dv ) dv v' Slope of the deflected curve θ v'≡ θ = arctan dx dx d 2v d 2v v'' Proportion to Bending Moment M ( v''≡ ) M = EI = − EI v'' dx2 dx2 3 3 d v d v = v''' Proportion to Shear Force V ( v'''≡ ) V = EI − EI v''' dx3 dx3 4 4 d v d v = EI v'''' Proportion to Distributed Load q ( v''''≡ ) q = −EI − v'''' dx4 dx4 Table 5.
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