w_2 The use of Ansys to calculate sandwich structures Vincent Manet Ecole des Mines de Saint-Etienne, Material and Mechanical Department, 158, cours Fauriel, 42023 Saint-Etienne cedex 2, France fax: (+33) 4-77-42-00-00, email: manet@emse.fr Abstract In this article, we make a comparative study on a simply supported sandwich beam

the span length.

In consequence, the beam is a five layer beam.

w_2

In this case, a moment is imposed in a single point of the beam, anywhere across the beam span.

The orientation of the triangular load is important!

W When the structure is 2-dimensional, and the imposed loads are exercised in the same 2D plane, there are just three resultant actions of interest: For a fixed beam, that is loaded by transverse loads only (so that their direction is perpendicular to the beam longitudinal axis), the axial force is always zero, provided the deflections remain small.

and

The dimensions of Optional properties, required only for deflection/slope results: Simply supported beam with uniform distributed load, Simply supported beam with point force in the middle, Simply supported beam with point force at a random position, Simply supported beam with triangular load, Simply supported beam with trapezoidal load, Simply supported beam with slab-type trapezoidal load distribution, Simply supported beam with partially distributed uniform load, Simply supported beam with partially distributed trapezoidal load, The material is homogeneous and isotropic (in other words its characteristics are the same in ever point and towards any direction), The loads are applied in a static manner (they do not change with time), The cross section is the same throughout the beam length.

However, as we move away, the predicted results become perfectly valid, as stated by the Saint-Venant principle, provided the loading area remains substantially smaller than the total beam length.

Restraining rotations results in zero slope at the two ends, as illustrated in the following figure.

Every cross-section that initially is plane and also normal to the longitudinal axis, remains plane and and normal to the deflected axis too. To the contrary, a structure that features more supports than required to restrict its free movements is called redundant or indeterminate structure. Instead, it is varying linearly, starting from zero at the left fixed end, gradually increasing, up to its peak value at the right end.

The load is distributed to a part of the beam span, having linearly varying magnitude from at the right end. , where

This load distribution is typical for the beams in the perimeter of a slab.

In order to consider the force as concentrated, though, the dimensions of the application area should be substantially smaller than the beam span length.

are force per length. ... (10 times or more) and also the cross-section is not multi layered (not a sandwich type section).

The following table presents the formulas describing the static response of a fixed beam, with both ends fixed, under a trapezoidal load distribution, as depicted in the schematic.

This is only a local phenomenon however, and as we move away from the force location, the discrepancy of the results becomes negligible.

are force per length.

Because there is so little guidance online, I am going to summarise what I think are a few key equations and principles of sandwich structures. In such system, analytical calculation of the maximum deflection is well-known (see attached).

and There are few textbook solutions available (again Zenkert has some simple cases). Because there is so little guidance online, t Fig.1 Schematic of a typical sandwich composite structure

, where are force per length.

Furthermore, the respective cases for fully loaded span, can be derived by setting The formulas for partially distributed uniform and triangular loads can be derived by appropriately setting the values of

The total amount of force applied to the beam is w_1

P

The orientation of the triangular load is important for the use of the table! w_1

The total amount of force applied to the beam is

The dimensions of

In the following table, the formulas describing the static response of the simple beam, under a partially distributed uniform load, are presented.

, imposed in the middle, are presented.

w

W=\left(L-a-b\right)w

and

The total amount of force applied to the beam is

As we move away from the force location, the discrepancy of the results becomes negligible. , where

The dimensions of

The dimensions of , imposed at a random distance the lengths at the left and right side of the beam respectively, where the load distribution is varying (triangular). The following table presents the formulas describing the static response of a fixed beam, with both ends fixed, under a uniform distributed load

w_2

In the close vicinity of the force, stress concentrations are expected and as result the response predicted by the classical beam theory maybe inaccurate.

The main goal of the study is to elaborate a mathematical model of this beam, analytical description and a solution of the three-point bending problem. It is not mandatory for the former to be smaller than the latter. The dimensions of the unloaded lengths at the left and right side of the beam respectively.

In the following table, the formulas describing the static response of the simple beam, under a partially distributed trapezoidal load, are presented.

L P The total amount of force applied to the beam is: are the unloaded lengths at the left and right side of the beam respectively. For the calculation of the internal forces and moments, at any section cut of the beam, a sign convention is necessary. or the distributed force per length

w

In the close vicinity of the force, stress concentrations are expected and as result the response predicted by the classical beam theory maybe inaccurate.

In this case, the force is concentrated in a single point, anywhere across the beam span. b Therefore, the simply supported beam offers no redundancy in terms of supports.

For the detailed terms of use click here. This is the most generic case.

.

In practice however, the force may be spread over a small area, although the dimensions of this area should be substantially smaller than the beam span length. and

and

W=w L The following are adopted here: These rules, though not mandatory, are rather universal.

M

The total amount of force applied to the beam is: The dimensions of

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