LIRALAND

Test 1.48. Rectangular plate simply supported at three corners and subjected to an out-of-plane concentrated load and concentrated moments

Updated Jun 12, 2026 | Published Sep 04, 2025

Objective

To determine the deformed state of a rectangular plate simply supported at three corners and subjected to an out-of-plane concentrated load and concentrated moments.

Reference

J.L. Batoz, An explicit formulation for an efficient triangular plate-bending element, International Journal for Numerical Methods in Engineering, vol.18, John Wiley and Sons, 1982.

Problem statement

A rectangular plate is simply supported at three corners (points A, B, and D). A concentrated load Fz, acting out of the plane of the plate, is applied at the free corner (point C). Pairs of concentrated moments Mx and My are applied at all four corners (points A, B, C, and D) and produce unidirectional bending in planes parallel to the corresponding sides of the plate.

Determine the out-of-plane displacement Z of corner C.

Design model

The design model is a beam grillage, slab.

Initial geometry

Initial geometry

Geometry

Plate thickness h = 1 m
Length of the longer side of the plate (along the X-axis of the global coordinate system) a = 40 m
Length of the shorter side of the plate (along the Y-axis of the global coordinate system) b = 20 m

Material properties

Modulus of elasticity Е = 1,0 * 103 Pa
Poisson's ratio ν = 0,3

Boundary conditions

The boundary conditions are provided by applying restraints in the Z degree of freedom at the plate corners located on the X and Y-axes of the global coordinate system (points A, B, and D).

Loads

Transverse concentrated load Fz=2 N;
Concentrated moments causing bending of the plate about the X-axis of the global coordinate system (bending about the short side) Mx=20 N*m;
Concentrated moments causing bending of the plate about the Y-axis of the global coordinate system (bending about the long side)My=40 N*m.

Output data

Design model

Design model

Deformed shape

Deformed shape

Mosaic plot of displacements along the global Z‑axis (w), m

Mosaic plot of displacements along the global Z‑axis (w), m

Comparison of calculation results

Parameter Theory LIRA-FEM Error, %
Displacement Z of the free vertex (point C), m -12,48 -12,48 0   

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